{"id":3204,"date":"2022-03-24T19:56:50","date_gmt":"2022-03-24T19:56:50","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3204"},"modified":"2023-06-22T15:40:26","modified_gmt":"2023-06-22T09:40:26","slug":"bohrs-atom-model","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/bohrs-atom-model\/","title":{"rendered":"\u09ac\u09cb\u09b0\u09c7\u09b0 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09ae\u09a1\u09c7\u09b2 (Bohr’s Atom Model)"},"content":{"rendered":"

1913<\/span> \u0996\u09cd\u09b0\u09bf\u09b8\u09cd\u099f\u09be\u09ac\u09cd\u09a6\u09c7 \u09a1\u09c7\u09a8\u09ae\u09be\u09b0\u09cd\u0995\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09bf\u09a6\u09cd\u09a7 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09a8\u09c0\u09b2\u09b8 \u09ac\u09cb\u09b0 (Niels Bohr) \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u098f\u0987 \u09ae\u09a1\u09c7\u09b2 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a4\u09be\u09ac \u0995\u09b0\u09c7\u09a8 \u098f\u09ac\u0982 <\/span>1922<\/span> \u0996\u09cd\u09b0\u09bf\u09b8\u09cd\u099f\u09be\u09ac\u09cd\u09a6\u09c7 \u098f\u0987 \u0986\u09ac\u09bf\u09b7\u09cd\u0995\u09be\u09b0\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09bf\u09a8\u09bf \u09a8\u09cb\u09ac\u09c7\u09b2 \u09aa\u09c1\u09b0\u09b8\u09cd\u0995\u09be\u09b0 \u09b2\u09be\u09ad \u0995\u09b0\u09c7\u09a8\u0964 \u09ac\u09cb\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a4\u09be\u09ac \u0995\u09b0\u09c7\u09a8 \u09af\u09c7, \u099a\u09bf\u09b0\u09be\u09af\u09bc\u09a4 \u09ac\u09b2\u09ac\u09bf\u09a6\u09cd\u09af\u09be (Classical mechanics) \u098f\u09ac\u0982 \u09ac\u09bf\u09a6\u09cd\u09af\u09c1\u09ce \u099a\u09c1\u09ae\u09cd\u09ac\u0995\u09a4\u09cd\u09ac (Electromagnetism)-\u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09a4\u09c7 \u09ac\u09bf\u0995\u09b2 \u09b9\u09af\u09bc\u09c7 (break down) \u09aa\u09a1\u09bc\u09c7\u0964 \u09a4\u09bf\u09a8\u09bf \u09ae\u09c2\u09b2\u09a4 \u09b0\u09be\u09a6\u09be\u09b0\u09ab\u09cb\u09b0\u09cd\u09a1\u09c7\u09b0 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09c0\u09af\u09bc \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09ae\u09a1\u09c7\u09b2\u09c7 \u0995\u09cb\u09af\u09bc\u09be\u09a8\u09cd\u099f\u09be\u09ae \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7\u09a8 \u098f\u09ac\u0982 \u0995\u09cb\u09af\u09bc\u09be\u09a8\u09cd\u099f\u09be\u09ae \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09c8\u09aa\u09cd\u09b2\u09ac\u09bf\u0995 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3 \u0998\u099f\u09bf\u09af\u09bc\u09c7 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09ac\u09b0\u09cd\u09a3\u09be\u09b2\u09bf \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u09c7\u09a8\u0964 \u09a4\u09be\u09b0 \u09a8\u09be\u09ae \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u098f\u0987 \u09ae\u09a1\u09c7\u09b2\u0995\u09c7 \u09ac\u09cb\u09b0 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09ae\u09a1\u09c7\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u098f\u0987 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09ae\u09a1\u09c7\u09b2\u09c7 \u09a4\u09bf\u09a8\u09bf \u09b0\u09be\u09a6\u09be\u09b0\u09ab\u09cb\u09b0\u09cd\u09a1\u09c7\u09b0 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09ae\u09a1\u09c7\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0985\u09b8\u09cd\u09a4\u09bf\u09a4\u09cd\u09ac\u09b8\u09b9 \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09a6\u09c2\u09b0 \u0995\u09b0\u09be\u09b0 \u099a\u09c7\u09b7\u09cd\u099f\u09be \u0995\u09b0\u09c7\u09a8\u0964 \u098f\u0987 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u09c7 \u09a8\u09c0\u09b2\u09b8 \u09ac\u09cb\u09b0 \u0995\u09cb\u09af\u09bc\u09be\u09a8\u09cd\u099f\u09be\u09ae \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7 \u09b8\u09ae\u09b8\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 \u0995\u09b0\u09a4\u09c7 \u099a\u09c7\u09b7\u09cd\u099f\u09be \u0995\u09b0\u09c7\u09a8\u0964 \u09a4\u09bf\u09a8\u09bf \u09b0\u09be\u09a6\u09be\u09b0\u09ab\u09cb\u09b0\u09cd\u09a1\u09c7\u09b0 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09ae\u09a1\u09c7\u09b2\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4 \u09ae\u09cc\u09b2\u09bf\u0995 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7\u09a8\u0964 \u098f\u0987 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09ac\u09cb\u09b0-\u098f\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u09ac\u09cb\u09b0-\u098f\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af\u09b8\u09ae\u09c2\u09b9 (Bohr’s theory)<\/b><\/h2>\n

\u0995. \u09aa\u09cd\u09b0\u09a5\u09ae \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af (\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4):<\/b><\/h3>\n

\u0995\u09cb\u09a8\u09cb \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8\u0995\u09be\u09b2\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ae\u09cb\u099f \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 \\frac{h}{2 \\pi}<\/span><\/span>-\u098f\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0997\u09c1\u09a3\u09bf\u09a4\u0995 \u09b9\u09ac\u09c7, \u0985\u09b0\u09cd\u09a5\u09be\u09ce L= \\frac{nh}{2 \\pi }<\/span><\/span> \u098f\u0996\u09be\u09a8\u09c7, h<\/span> \u09b9\u09b2\u09cb \u09aa\u09cd\u09b2\u09cd\u09af\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u0985\u09a8\u09cd\u09af\u09ad\u09be\u09ac\u09c7 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc, \u09af\u09c7 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0997\u09c1\u09b2\u09cb\u09a4\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 \\frac{h}{2 \\pi}<\/span><\/span>-\u098f\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3 \u0997\u09c1\u09a3\u09bf\u09a4\u0995, \u09b8\u09c7\u0997\u09c1\u09b2\u09cb\u0987 \u0985\u09a8\u09c1\u09ae\u09cb\u09a6\u09bf\u09a4 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0964<\/span><\/p>\n

\u098f\u09b0 \u0985\u09b0\u09cd\u09a5 \u098f\u0987 \u09af\u09c7 <\/span>r<\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0995\u0995\u09cd\u09b7\u09c7 <\/span>m<\/span><\/span> \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 <\/span>v<\/span><\/span> \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09a4\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09b2\u09c7 \u098f\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997, mvr=L= \\frac{nh}{2 \\pi}<\/span><\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7<\/span> n<\/span><\/span> \u098f\u0995\u099f\u09bf \u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0964 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u099c\u09a8\u09cd\u09af n<\/span>-\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09b9\u09af\u09bc\u0964 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u09c7\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09e7\u09ae, \u09e8\u09af\u09bc, \u09e9\u09af\u09bc \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u099c\u09a8\u09cd\u09af n=\u00a01,\u00a02,\u00a03<\/span><\/span>\u00a0<\/span>\u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09b9\u09af\u09bc; \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 <\/span>0<\/span><\/span> \u09a8\u09af\u09bc\u0964 n-<\/span><\/span>\u0995\u09c7 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u09ae\u09c1\u0996\u09cd\u09af \u0995\u09cb\u09af\u09bc\u09be\u09a8\u09cd\u099f\u09be\u09ae \u09b8\u0982\u0996\u09cd\u09af\u09be (Principal quantum number) \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (9.1) \u0995\u09c7 \u09ac\u09b2\u09be \u09b9\u09af\u09bc \u09ac\u09cb\u09b0\u09c7\u09b0 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 \u09b6\u09b0\u09cd\u09a4\u0964<\/span><\/p>\n

\u0996. \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af (\u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09cd\u09a4\u09b0 \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4):<\/b><\/h3>\n

\u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b8\u09cd\u09a5 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09b8\u09ae\u09c2\u09b9 \u0987\u099a\u09cd\u099b\u09be\u0995\u09c3\u09a4 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09ac \u09b8\u09ae\u09cd\u09ad\u09be\u09ac\u09cd\u09af \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09b0\u09a6\u09bf\u0995\u09c7 \u09aa\u09b0\u09bf\u09ad\u09cd\u09b0\u09ae\u09a3 \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be\u0964 \u09ac\u09b0\u0982 \u0995\u09af\u09bc\u09c7\u0995\u099f\u09bf \u09aa\u09c3\u09a5\u0995 \u09aa\u09c3\u09a5\u0995 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0993 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u09aa\u09b0\u09bf\u09ad\u09cd\u09b0\u09ae\u09a3 \u0995\u09b0\u09c7\u0964 \u098f\u0987 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0993 \u0985\u09ac\u09bf\u0995\u09bf\u09b0\u09a3\u09af\u09cb\u0997\u09cd\u09af \u0995\u0995\u09cd\u09b7\u09aa\u09a5 \u09ac\u09b2\u09c7\u0964 \u098f\u0987 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u0985\u09a8\u09c1\u09ae\u09cb\u09a6\u09bf\u09a4 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09b6\u0995\u09cd\u09a4\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7\u0964 \u098f\u099c\u09a8\u09cd\u09af \u098f\u0987 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09ac\u09be \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 <\/span>\u0995\u0995\u09cd\u09b7\u09aa\u09a5 (stationary or stable orbit) \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/b><\/p>\n

\u0997. \u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af (\u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4):<\/b><\/h3>\n

\u09af\u0996\u09a8\u0987 \u0995\u09cb\u09a8\u09cb \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u098f\u0995\u099f\u09bf \u09af\u09a5\u09cb\u09aa\u09af\u09cb\u0997\u09c0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5 \u09b9\u09a4\u09c7 \u0985\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u09af\u09a5\u09cb\u09aa\u09af\u09cb\u0997\u09c0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u09b2\u09be\u09ab \u09a6\u09c7\u09af\u09bc, \u09a4\u0996\u09a8\u0987 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09ac\u09bf\u0995\u09bf\u09b0\u09a3 \u09ac\u09be \u09b6\u09cb\u09b7\u09a8 \u0998\u099f\u09c7\u0964 \u09af\u09a6\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u0989\u099a\u09cd\u099a\u09a4\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09af\u09c1\u0995\u09cd\u09a4 \u0995\u0995\u09cd\u09b7\u09aa\u09a5 \u09b9\u09a4\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09a4\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09af\u09c1\u0995\u09cd\u09a4 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u09b2\u09be\u09ab \u09a6\u09c7\u09af\u09bc, \u09a4\u09ac\u09c7 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09ac\u09bf\u0995\u09bf\u09b0\u09a3 \u0998\u099f\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u0986\u09b0 \u09af\u09a6\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u09a8\u09bf\u09ae\u09cd\u09a8\u09a4\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09af\u09c1\u0995\u09cd\u09a4 \u0995\u0995\u09cd\u09b7\u09aa\u09a5 \u09b9\u09a4\u09c7 \u0989\u099a\u09cd\u099a\u09a4\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09af\u09c1\u0995\u09cd\u09a4 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u09b2\u09be\u09ab \u09a6\u09c7\u09af\u09bc \u09a4\u09ac\u09c7 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b6\u09cb\u09b7\u09a3 \u0998\u099f\u09c7\u0964 \u098f\u0987 \u09ac\u09bf\u0995\u09bf\u09b0\u09bf\u09a4 \u09ac\u09be \u09b6\u09cb\u09b7\u09bf\u09a4 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0993\u0987 \u09a6\u09c1\u099f\u09bf \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09ac\u09bf\u09af\u09bc\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u098f\u09ac\u0982 \u098f\u09b0 \u09ae\u09be\u09a8 \u098f\u0995 \u0995\u09cb\u09af\u09bc\u09be\u09a8\u09cd\u099f\u09be\u09ae \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>h\\nu <\/span><\/span>\u0964<\/span><\/p>\n

\u09ac\u09cb\u09b0 \u09ae\u09a1\u09c7\u09b2 \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09b9\u09be\u0987\u09a1\u09cd\u09b0\u09cb\u099c\u09c7\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u0993 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be\u00a0 (The radius and energy ratio of the hydrogen atom according to the Bohr model)<\/b><\/h2>\n

\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be<\/b><\/h3>\n

\u09b9\u09be\u0987\u09a1\u09cd\u09b0\u09cb\u099c\u09c7\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf \u09aa\u09cd\u09b0\u09cb\u099f\u09a8 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8 \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09a5\u09be\u0995\u09c7 \u098f\u09ac\u0982 \u098f\u0995\u099f\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 \u0998\u09cb\u09b0\u09c7\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ad\u09b0 m<\/span> \u098f\u09ac\u0982 \u099a\u09be\u09b0\u09cd\u099c e<\/span>\u09f7 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u099f\u09bf r \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u09aa\u09a5\u09c7 \u09aa\u09cd\u09b0\u09cb\u099f\u09a8 \u09a4\u09a5\u09be \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 v \u09ac\u09c7\u0997\u09c7 \u0998\u09c1\u09b0\u099b\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u0993\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2,<\/span><\/p>\n

\\mathrm{F}_{c}=\\frac{m v^{2}}{r}<\/span> \u00a0 <\/span>\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.3)<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0 \u09aa\u09cd\u09b0\u09cb\u099f\u09a8\u09c7\u09b0 \u099a\u09be\u09b0\u09cd\u099c \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09cb\u099f\u09a8 \u0993 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09b2,<\/span><\/p>\n

\\mathrm{F}_{e}=\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{e^{2}}{r^{2}}<\/span> \u00a0 <\/span>\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.4)<\/span><\/p>\n

\u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09b2\u0987 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2 \u09b8\u09b0\u09ac\u09b0\u09be\u09b9 \u0995\u09b0\u09c7, \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \\mathrm{F}_{C}=\\mathrm{F}_{e}<\/span><\/span>\u00a0 \u00a0 \u00a0\u00a0<\/span> \u00a0 <\/span>\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.5)<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (9.3) \u0993 (9.4) \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0987<\/span><\/p>\nm v^{2}=\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{e^{2}}{r}<\/span>\n

\u09ac\u09be, v=\\frac{e}{\\sqrt{4 \\pi \\epsilon_{0} m r}}<\/span><\/span>\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.6)<\/span><\/p>\n

n-\u09a4\u09ae \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u099c\u09a8\u09cd\u09af, v_{\\mathrm{n}}=\\frac{e}{\\sqrt{4 \\pi \\epsilon_{0} m r_{\\mathrm{n}}}}<\/span><\/span>\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.6a)<\/span><\/p>\n

\u09ac\u09cb\u09b0\u09c7\u09b0 \u09e7\u09ae \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/span><\/p>\nv_{\\mathrm{n}} m r_{n}=\\frac{n h}{2 \\pi}<\/span>\n

9.6(a) \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 -\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\u09ac\u09be, r_{\\mathrm{n}}=\\frac{n^{2} h^{2} \\epsilon_{0}}{\\pi m e^{2}}<\/span><\/span>\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.6b)<\/span><\/p>\n

[9.6(b)] \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09b2\u09cb <\/span>n<\/span>–<\/span>\u09a4\u09ae \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u0964 <\/span>n<\/span>=1<\/span> \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09b9\u09be\u0987\u09a1\u09cd\u09b0\u09cb\u099c\u09c7\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09e7\u09ae \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\n

r_{\\mathrm{n}}=\\frac{h^{2} \\epsilon_{0}}{\\pi m e^{2}}<\/span> \u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.6c)<\/span><\/p>\n

\u098f\u0987 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u099f\u09bf \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u09c7\u09b0 \u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u0995\u09be\u099b\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u098f\u0987 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0995\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u09ac\u09cb\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5 \u098f\u09ac\u0982 \u0995\u0995\u09cd\u09b7\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u0995\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u09ac\u09cb\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 9.6(c)-\u098f \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09b0\u09be\u09b6\u09bf\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 r_{1}=0.53 \\dot{A}<\/span><\/span>\u00a0\u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be<\/b><\/h3>\n

\u09b9\u09be\u0987\u09a1\u09cd\u09b0\u09cb\u099c\u09c7\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf\u09ae\u09be\u09a4\u09cd\u09b0 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u0986\u099b\u09c7\u0964 \u09a7\u09b0\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ae\u09cb\u099f \u09b6\u0995\u09cd\u09a4\u09bf\u00a0<\/span><\/p>\n

E_n=E_k+E_p<\/span>; \u098f\u0996\u09be\u09a8\u09c7 E_k=<\/span><\/span> \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u098f\u09ac\u0982 E_p=<\/span><\/span>\u00a0\u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf<\/span><\/p>\n=\\frac{1}{2} m v_{n}^{2}+(e V)<\/span>\n\\mathrm{E}_{n}=\\frac{1}{2} m v_{n}^{2}-\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{e^{2}}{r_{n}}<\/span>\n=\\frac{1}{2} m \\frac{e^{2}}{4 \\pi \\epsilon_{0} m r_{n}}-\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{e^{2}}{r_{n}}<\/span>\n

=\\frac{1}{2} \\frac{e^{2}}{4 \\pi \\epsilon_{0} r_{\\mathrm{n}}}-\\frac{1}{4 \\pi \\epsilon_{0}} \\frac{e^{2}}{r_{n}} \\quad\\left[v_{\\mathrm{n}}=\\frac{e}{\\sqrt{4 \\pi \\epsilon_{0} m r_{\\mathrm{n}}}}\\right]<\/span> \u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.7)<\/span><\/p>\n\\therefore \\mathrm{E}_{n}=\\frac{1}{4 \\pi \\epsilon_{0}} \\times e^{2}\\left[\\frac{1}{2 r_{\\mathrm{n}}}-\\frac{1}{r_{\\mathrm{n}}}\\right]<\/span>\n

=-\\frac{1}{2} \\times \\frac{1}{4 \\pi \\epsilon_{0}} \\times \\frac{e^{2}}{r_{\\mathrm{n}}}<\/span> \u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.8)<\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 <\/i>r_n<\/span><\/span>-\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987<\/span><\/i>,<\/span><\/p>\n

\\begin{aligned}\n\n\\mathrm{E}_{n} &=-\\frac{1}{2} \\times \\frac{1}{4 \\pi \\epsilon_{0}} \\times \\frac{e^{2} \\pi m e^{2}}{n^{2} h^{2} \\epsilon_{0}} \\quad\\left[r_{\\mathrm{n}}=\\frac{h^{2} \\epsilon_{0}}{\\pi m e^{2}}\\right] \\\\\n\n\\therefore \\mathrm{E}_{n} &=-\\frac{m e^{4}}{8 \\epsilon_{0}^{2} n^{2} h^{2}}\n\n\\end{aligned}<\/span> \u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.8a)<\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 <\/span>n=0,\u00a01,\u00a02,\u00a0...................n<\/span><\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09ae\u09cb\u099f \u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09b0\u09cd\u09ac\u09a6\u09be\u0987 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995<\/span>, <\/span><\/i>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0985\u09b8\u09c0\u09ae\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u0995\u09c7 \u09b8\u09b0\u09bf\u09af\u09bc\u09c7 \u09a8\u09bf\u09a4\u09c7 \u09b9\u09b2\u09c7 \u0995\u09be\u099c \u09b8\u09ae\u09cd\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc\u0964 \u098f\u09b0 \u0985\u09b0\u09cd\u09a5 \u09b9\u09b2\u09cb \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09a4\u09c7 \u0986\u09ac\u09a6\u09cd\u09a7\u0964<\/span><\/p>\n

n<\/span>=<\/span>\u00a0<\/span>1<\/span>\u00a0<\/span>\u09b9\u09b2\u09c7<\/span>, <\/span><\/i>9.4(<\/span>a)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0987<\/span>,\u00a0<\/span><\/i><\/p>\n

\\mathrm{E}_{n}=-\\frac{m e^{4}}{8 \\epsilon_{0}^{2} h^{2}}<\/span> \u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(9.8b)<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \\mathrm{E}_{n}=\\frac{1}{n^{2}} E_{1}, n=1<\/span><\/span>\u00a0\u09b9\u09b2\u09c7 \\mathrm{E}_{2}=\\frac{1}{4} E_{1}, n=3<\/span><\/span>\u00a0\u09b9\u09b2\u09c7 \\mathrm{E}_{3}=\\frac{1}{9} E_{1}<\/span><\/span>,\u00a0<\/span>\u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf\u0964\u00a0<\/span><\/p>\n

9.8(<\/span>b) <\/span><\/i>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc<\/span>,<\/span><\/i><\/p>\n\\begin{aligned}\n\n\\mathrm{E}_{1} &=-\\frac{\\left(9.1 \\times 10^{-31} \\mathrm{~kg}\\right)\\left(1.6 \\times 10^{-19} \\mathrm{C}\\right)^{4}}{8 \\times\\left(6.63 \\times 10^{-34} \\mathrm{Js}\\right)^{2}\\left(8.85 \\times 10^{-12} \\mathrm{C}^{2} \\mathrm{~N}^{-1} \\mathrm{~m}^{-2}\\right)^{2}} \\\\\n\n&=2.17 \\times 10^{-18} \\mathrm{~J}=-13.6 \\mathrm{eV}\n\n\\end{aligned}<\/span>\n

\u0987\u09b9\u09be \u09b9\u09be\u0987\u09a1\u09cd\u09b0\u09cb\u099c\u09c7\u09a8 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09ad\u09c2\u09ae\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09b6\u0995\u09cd\u09a4\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>9.4(<\/span>a)<\/span> \u0995\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc<\/span>, \\mathrm{E}_{n}=-\\frac{13.6}{n^{2}}<\/span><\/span><\/i>\u00a0\u09ac\u09be<\/span>, \\mathrm{E}_{n} \\propto \\frac{1}{n^{2}}<\/span><\/span><\/i>\u00a0\u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>n<\/span> <\/span><\/i>\u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09a4\u09c7 <\/span>E<\/span>–<\/span><\/i>\u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09ae \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09af\u09bc<\/span>, <\/span><\/i>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b6\u0995\u09cd\u09a4\u09bf \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09af\u09bc\u0964<\/span><\/p>\n

n<\/span>–<\/span><\/i>\u09a4\u09ae \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ac\u09c7\u0997 : \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>9.6(<\/span>a)<\/span> \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7 \u09ac\u09c7\u0997<\/span>, v_{n} \\propto \\frac{1}{\\sqrt{r_{n}}}<\/span><\/span><\/i><\/p>\n

\u0986\u09ac\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>9.6(<\/span>b)<\/span> \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7<\/span>, <\/span><\/i>\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7<\/span>, r_{n} \\propto n^{2}<\/span><\/span><\/i><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982<\/span>, v_{n} \\propto \\frac{1}{\\sqrt{n^{2}}} \\propto \\frac{1}{n} <\/span><\/span><\/i>\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>n-<\/span><\/i>\u098f\u09b0 \u09ae\u09be\u09a8 \u09af\u09a4 \u09ac\u09be\u09a1\u09bc\u09ac\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ac\u09c7\u0997 \u09a4\u09a4 \u0995\u09ae\u09ac\u09c7\u0964 <\/span>n=1<\/span><\/span>, <\/span><\/i>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09cd\u09b0\u09a5\u09ae \u09ac\u09cb\u09b0 \u0995\u0995\u09cd\u09b7\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ac\u09c7\u0997 v_1<\/span><\/span>\u00a0\u09b8\u09ac\u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf\u0964<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>9.6(<\/span>a)<\/span>–<\/span><\/i>\u098f <\/span>n=1<\/span><\/span> \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987<\/span>, v_{\\mathrm{n}}=\\frac{e}{\\sqrt{4 \\pi \\epsilon_{0} m r_{\\mathrm{n}}}}<\/span><\/span><\/i>\u0964 \u098f\u0996\u09a8 r=0.53 A=0.53 \\times 10^{-10} \\mathrm{~m}<\/span><\/span>\u00a0\u098f\u09ac\u0982 \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc<\/span>, v_{1}=2.18 \\times 10^{6} \\mathrm{~ms}^{-1}<\/span><\/span><\/i>\u0964<\/span> \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u098f\u0987 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u0986\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997 3 \\times 10^{10}\u00a0ms^{-1}<\/span><\/span>\u00a0\u098f\u09b0 \u09aa\u09cd\u09b0\u09be\u09af\u09bc <\/span>137<\/span> \u09ad\u09be\u0997\u09c7\u09b0 <\/span>1<\/span> \u09ad\u09be\u0997\u0964<\/span><\/p>\n

\u09ac\u09cb\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0997\u09c1\u09b2\u09bf\u0995\u09c7 \u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5 \u09ac\u09b2\u09be \u09b9\u09af\u09bc \u0995\u09c7\u09a8<\/b> ?<\/i><\/b><\/h3>\n

\u09ac\u09cb\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0997\u09c1\u09b2\u09bf\u0995\u09c7 \u2018\u09b8\u09cd\u09a5\u09be\u09af\u09bc\u09c0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u2019 \u09ac\u09b2\u09be \u09b9\u09af\u09bc \u0995\u09be\u09b0\u09a3 \u098f\u0987 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u0997\u09c1\u09b2\u09bf\u09a4\u09c7 \u09aa\u09cd\u09b0\u09a6\u0995\u09cd\u09b7\u09bf\u09a3 \u0995\u09b0\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u0995\u09cb\u09a8\u09cb \u09b6\u0995\u09cd\u09a4\u09bf \u09ac\u09bf\u0995\u09bf\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a8\u09be\u0964 \u09af\u09a6\u09bf\u0993 \u09aa\u09cd\u09b0\u09a6\u0995\u09cd\u09b7\u09bf\u09a3 \u0995\u09be\u09b2\u09c7 \u098f\u09a6\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09a5\u09be\u0995\u09c7 \u09a4\u09a5\u09be\u09aa\u09bf \u09ac\u09cb\u09b0\u09c7\u09b0 \u09b8\u09cd\u09ac\u09c0\u0995\u09be\u09b0\u09cd\u09af \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u0997\u09c1\u09b2\u09bf \u09b6\u0995\u09cd\u09a4\u09bf \u0995\u09cd\u09b7\u09af\u09bc \u09a8\u09be \u0995\u09b0\u09c7 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09b0\u09a6\u09bf\u0995\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u0998\u09c2\u09b0\u09cd\u09a3\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u09c0\u09af\u09bc \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2\u09c7\u09b0 \u0989\u09ce\u09b8 \u0995\u09c0<\/b> ?<\/i><\/b><\/h3>\n

\u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09b0\u09a6\u09bf\u0995\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u0998\u09c2\u09b0\u09cd\u09a3\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u09c0\u09af\u09bc \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2\u09c7\u09b0 \u0989\u09ce\u09b8 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09bf\u09af\u09bc\u09be\u09b8\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a7\u09a8\u099a\u09be\u09b0\u09cd\u099c \u098f\u09ac\u0982 \u098f\u09b0 \u099a\u09be\u09b0\u09a6\u09bf\u0995\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u09ae\u09be\u09a8 \u098b\u09a3\u099a\u09be\u09b0\u09cd\u099c\u09af\u09c1\u0995\u09cd\u09a4 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u0993\u09aa\u09b0 \u0995\u09c1\u09b2\u09ae\u09cd\u09ac\u09c0\u09af\u09bc \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a4\u09a1\u09bc\u09bf\u09ce \u09ac\u09b2\u0987 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2 \u09b8\u09b0\u09ac\u09b0\u09be\u09b9 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

1913 \u0996\u09cd\u09b0\u09bf\u09b8\u09cd\u099f\u09be\u09ac\u09cd\u09a6\u09c7 \u09a1\u09c7\u09a8\u09ae\u09be\u09b0\u09cd\u0995\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09bf\u09a6\u09cd\u09a7 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09a8\u09c0\u09b2\u09b8 \u09ac\u09cb\u09b0 (Niels Bohr) \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u098f\u0987 \u09ae\u09a1\u09c7\u09b2 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a4\u09be\u09ac \u0995\u09b0\u09c7\u09a8 \u098f\u09ac\u0982 1922 \u0996\u09cd\u09b0\u09bf\u09b8\u09cd\u099f\u09be\u09ac\u09cd\u09a6\u09c7 \u098f\u0987 \u0986\u09ac\u09bf\u09b7\u09cd\u0995\u09be\u09b0\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09bf\u09a8\u09bf \u09a8\u09cb\u09ac\u09c7\u09b2 \u09aa\u09c1\u09b0\u09b8\u09cd\u0995\u09be\u09b0 \u09b2\u09be\u09ad \u0995\u09b0\u09c7\u09a8\u0964 \u09ac\u09cb\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a4\u09be\u09ac \u0995\u09b0\u09c7\u09a8 \u09af\u09c7, \u099a\u09bf\u09b0\u09be\u09af\u09bc\u09a4 \u09ac\u09b2\u09ac\u09bf\u09a6\u09cd\u09af\u09be (Classical mechanics) \u098f\u09ac\u0982 \u09ac\u09bf\u09a6\u09cd\u09af\u09c1\u09ce \u099a\u09c1\u09ae\u09cd\u09ac\u0995\u09a4\u09cd\u09ac (Electromagnetism)-\u098f\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09b8\u09ae\u09c2\u09b9 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09a4\u09c7 \u09ac\u09bf\u0995\u09b2<\/p>\n

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