{"id":2853,"date":"2022-03-24T16:20:20","date_gmt":"2022-03-24T16:20:20","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2853"},"modified":"2022-03-24T11:08:19","modified_gmt":"2022-03-24T11:08:19","slug":"mean-free-path-and-degrees-of-freedom","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/mean-free-path-and-degrees-of-freedom\/","title":{"rendered":"\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09ac\u09be \u0997\u09dc \u09a8\u09bf\u09b0\u09cd\u09ac\u09be\u09a7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u098f\u09ac\u0982 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be (Mean Free Path And Degrees of Freedom)"},"content":{"rendered":"

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09ac\u09be \u0997\u09dc \u09a8\u09bf\u09b0\u09cd\u09ac\u09be\u09a7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/b>(Mean Free Path)<\/b><\/h2>\n

\u09b8\u0982\u099c\u09cd\u099e\u09be:<\/b> \u0995\u09cb\u09a8\u09cb \u0985\u09a3\u09c1\u09b0 \u09aa\u09b0\u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0997\u09c1\u09b2\u09cb\u09b0 \u0997\u09dc \u09a8\u09bf\u09b2\u09c7 \u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df \u09a4\u09be\u0995\u09c7\u0987 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 (Mean Free Path)<\/strong> \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u09af\u09a6\u09bf <\/span>N<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09a7\u09be\u0995\u09cd\u0995\u09be\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0985\u09a3\u09c1 \u09ae\u09cb\u099f l<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u09a4\u09ac\u09c7 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5, \\lambda=\\frac{l}{N}<\/span><\/span>\u0964<\/span><\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf \u098f\u0995\u0995 \u0986\u09df\u09a4\u09a8\u09c7 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>n<\/span> \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09ac\u09cd\u09af\u09be\u09b8 \\sigma<\/span><\/span>\u0964 \u0986\u09ae\u09b0\u09be \u09af\u09c7 \u0985\u09a3\u09c1\u099f\u09bf\u09b0 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u099b\u09bf \u09b9\u09bf\u09b8\u09be\u09ac\u09c7\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09c7\u09ac\u09b2\u09ae\u09be\u09a4\u09cd\u09b0 \u09b8\u09c7 \u0985\u09a3\u09c1\u099f\u09bf\u0995\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09a7\u09b0\u09c7 \u09ac\u09be\u0995\u09bf \u0985\u09a3\u09c1\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u099b\u09bf\u0964<\/span><\/p>\n

\"Mean<\/p>\n

(\u09e7\u09e6.\u09e7\u09e6) \u099a\u09bf\u09a4\u09cd\u09b0\u09c7 \u0986\u09ae\u09b0\u09be <\/span>C<\/span> \u0985\u09a3\u09c1\u099f\u09bf\u09b0 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09a4\u09c7 \u099a\u09be\u0987\u0964 <\/span>C<\/span> \u0985\u09a3\u09c1\u099f\u09bf l<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09be\u09b0 \u09b8\u09ae\u09df \u0985\u09a8\u09cd\u09af \u09af\u09c7 \u09b8\u0995\u09b2 \u0985\u09a3\u09c1\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <\/span>C<\/span> \u0985\u09a3\u09c1\u099f\u09bf\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \\sigma<\/span>\u00a0<\/span> \u09a6\u09c2\u09b0\u09c7, (\u099a\u09bf\u09a4\u09cd\u09b0\u09c7 <\/span>A<\/span> \u0993 <\/span>B<\/span> \u0985\u09a3\u09c1\u09a6\u09cd\u09ac\u09df) \u0985\u09a5\u09ac\u09be \\sigma<\/span>\u00a0<\/span> \u0985\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09ae \u09a6\u09c2\u09b0\u09c7 \u09a5\u09be\u0995\u09ac\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09a7\u09be\u0995\u09cd\u0995\u09be \u0996\u09be\u09ac\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \\sigma<\/span>\u00a0<\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u0993 l<\/span>\u00a0<\/span> \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09b8\u09bf\u09b2\u09bf\u09a8\u09cd\u09a1\u09be\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09af\u09c7 \u09b8\u0995\u09b2 \u0985\u09a3\u09c1\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a5\u09be\u0995\u09ac\u09c7 <\/span>C<\/span> \u0985\u09a3\u09c1\u099f\u09bf \u0995\u09c7\u09ac\u09b2\u09ae\u09be\u09a4\u09cd\u09b0 \u09a4\u09be\u09a6\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09a7\u09be\u0995\u09cd\u0995\u09be \u0996\u09be\u09ac\u09c7\u0964 \u098f \u09b8\u09bf\u09b2\u09bf\u09a8\u09cd\u09a1\u09be\u09b0\u09c7\u09b0 \u0986\u09df\u09a4\u09a8 \\pi \\sigma^{2} l<\/span><\/span>\u0964 \u098f\u0996\u09a8 \u098f\u0995\u0995 \u0986\u09df\u09a4\u09a8\u09c7 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>n<\/span> \u09b9\u09b2\u09c7 <\/span>\\pi \\sigma^{2} l<\/span><\/span> \u0986\u09df\u09a4\u09a8\u09c7 \u09ae\u09cb\u099f \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09b9\u09ac\u09c7 n \\pi \\sigma^{2} l<\/span>l<\/span> \u0985\u09b0\u09cd\u09a5\u09be\u09ce l<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09be\u09b0 \u09b8\u09ae\u09df <\/span>C<\/span> \u0985\u09a3\u09c1\u099f\u09bf n \\pi \\sigma^{2} l<\/span><\/span>l<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09ac\u09be\u09b0 \u09a7\u09be\u0995\u09cd\u0995\u09be \u0996\u09be\u09ac\u09c7\u0964<\/span><\/p>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u0995\u09cb\u09a8\u09cb \u0985\u09a3\u09c1\u09b0 \u09aa\u09b0 \u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0997\u09c1\u09b2\u09cb\u09b0 \u0997\u09dc \u09a8\u09bf\u09b2\u09c7 \u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df \u09a4\u09be\u0995\u09c7 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5, \\lambda=\\frac{\\text { \u0985\u09a4\u09bf\u09a4\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac }}{\\text { \u09a7\u09be\u0995\u09cd\u0995\u09be \u09b8\u0982\u0996\u09cd\u09af\u09be }}=\\frac{l}{n \\pi \\sigma^{2} l}<\/span><\/span><\/p>\n

\\therefore \\lambda=\\frac{1}{n \\pi \\sigma^{2}}<\/span> …\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 (10.28)<\/p>\n

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u0986\u09a3\u09ac\u09bf\u0995 \u09ac\u09cd\u09af\u09be\u09b8 \\sigma<\/span><\/strong>\u00a0<\/span>, <\/b> \u0993 \u098f\u0995\u0995 \u0986\u09df\u09a4\u09a8\u09c7 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/b>n<\/strong>–<\/span>\u098f\u09b0 \u0989\u09aa\u09b0\u09bf\u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09c7\u09a8 \u0995\u09cd\u09b2\u09be\u09b8\u09bf\u09df\u09be\u09b8\u0964<\/b><\/h3>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u098f\u0995\u099f\u09bf \u0985\u09a3\u09c1\u09b0 \u09ad\u09b0 <\/span>=m<\/span>\u0964 \u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u098f\u0995\u0995 \u0986\u09df\u09a4\u09a8\u09c7 \u0985\u09a3\u09c1\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>n,<\/span> \u0995\u09be\u099c\u09c7\u0987 \u098f\u0995\u0995 \u0986\u09df\u09a4\u09a8\u09c7 \u0985\u09a3\u09c1\u09b0 \u09ad\u09b0 <\/span>=mn=<\/span> \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac <\/span>\u0964 <\/span>(10.28)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b9\u09b0 \u0993 \u09b2\u09ac\u0995\u09c7 <\/span>m<\/span> \u09a6\u09bf\u09df\u09c7 \u0997\u09c1\u09a3 \u0995\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n\\lambda=\\frac{m}{\\pi \\sigma^{2} m n}=\\frac{m}{\\pi \\sigma^{2} \\rho}<\/span>\n

\u09ac\u09be, \\lambda \\propto \\frac{1}{\\rho} \\quad<\/span><\/span>\u00a0 \u00a0[\u098f\u0996\u09be\u09a8\u09c7 <\/span>K<\/span> \u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac\u0995]<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac, \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u098f\u09ac\u0982 \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0995\u09be\u099c\u09c7\u0987 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u099a\u09be\u09aa\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u098f\u09ac\u0982 \u09aa\u09b0\u09ae \u09a4\u09be\u09aa\u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/span><\/p>\n

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5\u09c7\u09b0 \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be <\/b>(Other equations of mean free path)<\/b><\/h3>\n

\u0995\u09cd\u09b2\u09be\u09b8\u09bf\u09df\u09be\u09b8\u09c7\u09b0 \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09a4\u09c7 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u0997\u09a3\u09a8\u09be \u09a8\u09bf\u09b0\u09cd\u09ad\u09c1\u09b2 \u09a8\u09df\u0964 \u0995\u09be\u09b0\u09a3, \u09af\u09c7 \u0985\u09a3\u09c1\u09b0 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09b9\u09df\u09c7\u099b\u09c7 \u09b8\u09c7\u099f\u09bf \u099b\u09be\u09dc\u09be \u0985\u09a8\u09cd\u09af \u0985\u09a3\u09c1\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a7\u09b0\u09be \u09b9\u09df\u09c7\u099b\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09aa\u0995\u09cd\u09b7\u09c7 \u09b8\u0995\u09b2 \u0985\u09a3\u09c1\u0987 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964 \u09ac\u09cb\u09b2\u09cd\u200c\u099c\u09ae\u09cd\u09af\u09be\u09a8<\/strong> \u09b8\u0995\u09b2 \u0985\u09a3\u09c1\u09b0 \u0997\u09dc\u09ac\u09c7\u0997 \u09b8\u09ae\u09be\u09a8 \u09a7\u09b0\u09c7 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09c7\u09a8,<\/span><\/p>\n

\\lambda=\\frac{3}{4 \\pi \\sigma^{2} n}<\/span> …\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 (10.29)<\/p>\n

\u09aa\u09b0\u09c7 \u09ae\u09cd\u09af\u09be\u0995\u09cd\u09b8\u0993\u09df\u09c7\u09b2 \u09a4\u09be\u0981\u09b0 \u09ac\u09c7\u0997 \u09ac\u09a3\u09cd\u099f\u09a8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09c7\u09a8,<\/span><\/p>\n

\\lambda=\\frac{1}{\\sqrt{2} \\pi \\sigma^{2} n}<\/span> …\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 (10.30)<\/p>\n

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4\u09aa\u09a5 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df\u09c7\u09b0 \u099c\u09a8\u09cd\u09af\u09c7 \\lambda=\\frac{1}{\\sqrt{2} \\pi \\sigma^{2} n}<\/span><\/span>\u00a0\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09be \u09b9\u09df\u09c7 \u09a5\u09be\u0995\u09c7\u0964<\/span><\/p>\n

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u0995\u09cd\u09b2\u09be\u09b8\u09bf\u09df\u09be\u09b8 \u0993 \u09ac\u09cb\u09b2\u099c\u09ae\u09cd\u09af\u09be\u09a8\u09c7\u09b0 \u0993 \u09ae\u09cd\u09af\u09be\u0995\u09cd\u09b8\u0993\u09df\u09c7\u09b2\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a4\u09c1\u09b2\u09a8\u09be \u0995\u09b0\u0964<\/b><\/h3>\n

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4\u09aa\u09a5\u09c7\u09b0 \u0995\u09cd\u09b2\u09be\u09b8\u09bf\u09df\u09be\u09b8\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7<\/span>–<\/span><\/p>\n

\\lambda_{C}=\\frac{1}{n \\pi \\sigma^{2}}<\/span> …\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 (10.31)<\/p>\n

\u098f\u09ac\u0982 \u09ac\u09cb\u09b2\u099c\u09ae\u09cd\u09af\u09be\u09a8\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7,\u00a0<\/span><\/p>\n

\\lambda_{B}=\\frac{3}{4 n \\pi \\sigma^{2}}<\/span> …\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 \u00a0…\u00a0 (10.32)<\/p>\n

\u098f\u09ac\u0982 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4\u09aa\u09a5\u09c7\u09b0 \u09ae\u09cd\u09af\u09be\u0995\u09cd\u09b8\u0993\u09df\u09c7\u09b2\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7,\u00a0\u00a0<\/span><\/p>\n\\begin{aligned}\n\n\\lambda_{M} &=\\frac{1}{\\sqrt{2} n \\pi \\sigma^{2}} \\\\ ...\u00a0 \u00a0...\u00a0 \u00a0...\u00a0 \u00a0...\u00a0 (10.33)\n\n\\therefore \\frac{\\lambda_{C}}{\\lambda_{B}} &=\\frac{1}{n \\pi \\sigma^{2}} \\div \\frac{3}{4 n \\pi \\sigma^{2}}=\\frac{4}{3}\n\n\\end{aligned}\\\\<\/span>\n \\lambda_{C}: \\lambda_{B}=4: 3 \\\\<\/span>\n\\quad \\frac{\\lambda_{C}}{\\lambda_{M}}=\\frac{1}{n \\pi \\sigma^{2}} \\div \\frac{1}{\\sqrt{2} n \\pi \\sigma^{2}}=\\sqrt{2}\\\\<\/span>\n\\lambda_{C}: \\lambda_{M}=\\sqrt{2}: 1<\/span>\n

\u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be <\/b>(Degrees of Freedom)<\/b><\/h2>\n

\u09b8\u0982\u099c\u09cd\u099e\u09be:<\/b> \u0995\u09cb\u09a8\u09cb \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b8\u09bf\u09b8\u09cd\u099f\u09c7\u09ae\u09c7\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3\u09ad\u09be\u09ac\u09c7 \u09ac\u09cb\u099d\u09be\u09a4\u09c7 \u09ae\u09cb\u099f \u09af\u09c7 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8 \u09b0\u09be\u09b6\u09bf\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u09b9\u09df \u09a4\u09be\u0995\u09c7 \u09ac\u09be \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b8\u09bf\u09b8\u09cd\u099f\u09c7\u09ae\u09c7\u09b0 \u09ae\u09cb\u099f \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be\u09df \u09af\u09c7 \u0995\u09df\u099f\u09bf \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8 \u09ac\u09b0\u09cd\u0997 \u09b0\u09be\u09b6\u09bf \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df \u09b8\u09c7\u0987 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be<\/strong> \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u0995\u09cb\u09a8\u09cb \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b8\u09bf\u09b8\u09cd\u099f\u09c7\u09ae\u09c7\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3\u09b0\u09c2\u09aa\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09a4\u09c7 \u09af\u09a4\u0997\u09c1\u09b2\u09cb \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u09b9\u09df \u09a4\u09be\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0987 \u09b9\u099a\u09cd\u099b\u09c7 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u0964<\/b><\/h3>\n

\u0995\u09cb\u09a8\u09cb \u09b8\u09bf\u09b8\u09cd\u099f\u09c7\u09ae\u09c7\u09b0 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>=<\/span> \u09b8\u09bf\u09b8\u09cd\u099f\u09c7\u09ae\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u0997\u09c1\u09b2\u09cb\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3\u09b0\u09c2\u09aa\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09a4\u09c7 \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8\u09c0\u09df \u09ae\u09cb\u099f \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u098f\u09ac\u0982 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u0997\u09c1\u09b2\u09cb\u09b0 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u09ad\u09bf\u09a4\u09b0 \u09b8\u09cd\u09ac\u09a4\u09a8\u09cd\u09a4\u09cd\u09b0\u09ad\u09be\u09ac\u09c7 \u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09b0\u09df\u09c7\u099b\u09c7 \u09a4\u09be\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0 \u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u0964\u00a0<\/span><\/p>\n

\u0995\u09cb\u09a8\u09cb \u0997\u09cd\u09af\u09be\u09b8 \u0985\u09a3\u09c1\u09a4\u09c7 <\/span>x<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09a5\u09be\u0995\u09b2\u09c7 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09b0\u09cd\u09ac\u09be\u09a7\u09bf\u0995 \u09b9\u09ac\u09c7 <\/span>3x<\/span>\u0964 \u098f\u0996\u09a8 \u098f\u0995 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09c7\u09b2\u09be\u09df <\/span>x=1,<\/span> \u0995\u09be\u099c\u09c7\u0987 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b9\u09ac\u09c7 <\/span>3<\/span>\u0964 \u09a6\u09cd\u09ac\u09bf-\u09aa\u09be\u09b0\u09ae\u09be\u09a3\u09ac\u09bf\u0995 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09ac\u09c7\u09b2\u09be\u09df <\/span>x=2,<\/span> \u0995\u09be\u099c\u09c7\u0987 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b9\u0993\u09df\u09be \u0989\u099a\u09bf\u09a4 <\/span>3\u00d72=6<\/span>\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09a6\u09c1\u099f\u09bf \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u099c\u09be\u09df \u09b0\u09be\u0996\u09be\u09df \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09a6\u09c1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09a5\u09be\u0995\u09be\u09df \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b9\u09ac\u09c7 <\/span>3\u00d72-1<\/span>=5<\/span>\u0964 \u09ac\u09b9\u09c1 \u09aa\u09be\u09b0\u09ae\u09be\u09a3\u09ac\u09bf\u0995 \u09af\u09c7\u09ae\u09a8 \u09a4\u09cd\u09b0\u09bf-\u09aa\u09be\u09b0\u09ae\u09be\u09a3\u09ac\u09bf\u0995 \u0997\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1 \u09a4\u09bf\u09a8\u099f\u09bf, \u0985\u09a3\u09c1\u09b0 \u09ad\u09bf\u09a4\u09b0\u09c7 \u09a6\u09c1\u09ad\u09be\u09ac\u09c7 \u09b8\u099c\u09cd\u099c\u09bf\u09a4 \u09a5\u09be\u0995\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09af\u09c7\u09ae\u09a8 \u09ae\u09be\u099d\u0996\u09be\u09a8\u09c7 \u098f\u0995\u099f\u09bf \u098f\u09ac\u0982 \u09a6\u09c1\u09aa\u09be\u09b6\u09c7 \u09a6\u09c1\u099f\u09bf \u09ac\u09be \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u09a4\u09bf\u09a8 \u0995\u09cb\u09a3\u09c7 \u09a4\u09bf\u09a8\u099f\u09bf\u0964 \u09aa\u09cd\u09b0\u09a5\u09ae \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8\u09a4\u09be\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b9\u09ac\u09c7 <\/span>3\u00d73-2<\/span>=7<\/span> \u098f\u09ac\u0982 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b9\u09ac\u09c7 <\/span>3\u00d73-3<\/span>=6<\/span>\u0964<\/span><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 \u09ac\u09be \u0997\u09dc \u09a8\u09bf\u09b0\u09cd\u09ac\u09be\u09a7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac (Mean Free Path) \u09b8\u0982\u099c\u09cd\u099e\u09be: \u0995\u09cb\u09a8\u09cb \u0985\u09a3\u09c1\u09b0 \u09aa\u09b0\u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0997\u09c1\u09b2\u09cb\u09b0 \u0997\u09dc \u09a8\u09bf\u09b2\u09c7 \u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09df \u09a4\u09be\u0995\u09c7\u0987 \u0997\u09dc \u09ae\u09c1\u0995\u09cd\u09a4 \u09aa\u09a5 (Mean Free Path) \u09ac\u09b2\u09c7\u0964 \u09af\u09a6\u09bf N \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09a7\u09be\u0995\u09cd\u0995\u09be\u09b0 \u09ad\u09c7\u09a4\u09b0 \u0985\u09a3\u09c1 \u09ae\u09cb\u099f \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[51,4244,3028,50],"tags":[2054,2053,2051,2050,2052],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2853"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=2853"}],"version-history":[{"count":11,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2853\/revisions"}],"predecessor-version":[{"id":7948,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2853\/revisions\/7948"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2853"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2853"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}