{"id":3214,"date":"2022-03-24T18:55:12","date_gmt":"2022-03-24T18:55:12","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3214"},"modified":"2022-03-24T13:40:35","modified_gmt":"2022-03-24T13:40:35","slug":"3214-2","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/3214-2\/","title":{"rendered":"\u09ad\u09b0-\u09b6\u0995\u09cd\u09a4\u09bf (Mass Energy)"},"content":{"rendered":"

\u09ad\u09b0-\u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (<\/b>Mass-energy relation<\/b>)<\/b><\/h2>\n

\u0986\u0987\u09a8\u09b8\u09cd\u099f\u09be\u0987\u09a8-\u098f\u09b0 \u09ad\u09b0-\u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09b9\u09b2\u09cb \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7\u09b0 \u0995\u09be\u09b2\u099c\u09df\u09c0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0964 \u0986\u0987\u09a8\u09b8\u09cd\u099f\u09be\u0987\u09a8 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u098f\u0987 \u09ac\u09bf\u0996\u09cd\u09af\u09be\u09a4 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09c7\u09a8\u0964 \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0\u0995\u09c7 \u09ad\u09b0-\u09b6\u0995\u09cd\u09a4\u09bf \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u0993 \u09ac\u09b2\u09c7\u0964 \u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u0997\u09a4\u09bf \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u09b9\u09be\u09b0\u0995\u09c7 \u09ac\u09b2 \u09ac\u09b2\u09c7\u0964 \u0985\u09a4\u098f\u09ac,\u00a0\u00a0<\/span><\/p>\n

\\mathrm{F}=\\frac{d}{d t}(\\mathrm{~m} \\vartheta)<\/span>\u00a0 \u2026\u00a0 \u2026\u00a0 \u00a0\u00a0 [8.38]\u00a0<\/span><\/p>\n

\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u09ad\u09b0 \u098f\u09ac\u0982 \u09ac\u09c7\u0997 \u0989\u09ad\u09df\u0987 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2\u0964<\/span><\/p>\n

\\begin{aligned}\n\n\\therefore \\mathrm{F} &=\\frac{d}{d t}(\\mathrm{~m} \\vartheta) \\\\\n\n&=\\mathrm{m} \\frac{d \\vartheta}{d t}+\\vartheta \\frac{d m}{d t}\n\n\\end{aligned}<\/span>\u2026\u00a0 \u00a0\u00a0\u00a0 \u2026\u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[8.39]<\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u09ac\u09b2 F \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 dx \u09b8\u09b0\u09a3 \u0998\u099f\u09be\u09df\u0964 \u0985\u09a4\u098f\u09ac \u0995\u09c3\u09a4 \u0995\u09be\u099c = F.dx\u0964 \u098f\u0987 \u0995\u09be\u099c \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n

\\therefore \\mathrm{dE}_{\\mathrm{k}}<\/span>= F.dx<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \\begin{array}{l}\n\n=\\left(\\mathrm{m} \\frac{d \\vartheta}{d t}+\\vartheta \\frac{d m}{d t}\\right) \\cdot \\mathrm{dx} \\\\\n\n=\\mathrm{m} \\cdot \\frac{d \\vartheta}{d t} \\cdot \\mathrm{dx}+\\vartheta \\cdot \\frac{d m}{d t} \\cdot \\mathrm{dx} \\\\\n\n=\\mathrm{m} \\vartheta \\cdot \\mathrm{d} \\vartheta+\\vartheta^{2} d m\n\n\\end{array}<\/span>\u2026\u00a0 \u2026\u00a0 \u00a0 \u00a0\u00a0\u00a0[8.40]<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\\left[\\because \\frac{\\mathrm{dx}}{d t}=\\vartheta\\right]<\/span><\/span>\u00a0<\/span>\u00a0<\/span><\/p>\n

\u098f\u0996\u09a8 \u09ad\u09b0 <\/span>\u0993 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/p>\n

\\mathrm{m}=\\frac{\\mathrm{m}_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span> \u2026\u00a0 \u2026\u00a0 \u00a0\u00a0 [8.41]<\/span><\/p>\n

\u0989\u09ad\u09df \u09aa\u09be\u09b6\u09c7 \u09ac\u09b0\u09cd\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\\begin{array}{l}\n\n\\mathrm{m}^{2}=\\frac{\\mathrm{m}_{0}^{2}}{1-\\vartheta^{2} \/ c^{2}} \\\\\n\n\\text { \u09ac\u09be, } \\mathrm{m}^{2}=\\frac{\\mathrm{m}_{0}^{2} c^{2}}{c^{2}-\\vartheta^{2}} \\\\\n\n\\text { \u09ac\u09be, } \\mathrm{m}^{2} c^{2}-\\mathrm{m}^{2} \\vartheta^{2}=\\mathrm{m}_{0}^{2} c^{2} \\\\\n\n\\text { \u09ac\u09be, } \\mathrm{m}^{2} c^{2}=\\mathrm{m}^{2} \\vartheta^{2}+\\mathrm{m}_{0}^{2} c^{2}\n\n\\end{array}<\/span> \u2026\u00a0 \u2026\u00a0 \u00a0\u00a0 [8.42]<\/p>\n

 <\/p>\n

\u0989\u09ad\u09af\u09bc \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac\u0995\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u09c0\u0995\u09b0\u09a3 \u09ac\u09be \u0985\u09ac\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n2 \\mathrm{~m} \\cdot \\mathrm{dm} c^{2}=2 \\mathrm{~m} \\cdot \\mathrm{dm} \\vartheta^{2}+2 \\vartheta \\cdot \\mathrm{d} \\vartheta \\mathrm{m}^{2} \\\\<\/span>\n

\u09ac\u09be, \\mathrm{dm} \\cdot c^{2}=\\left(\\mathrm{m} \\vartheta \\cdot \\mathrm{d} \\vartheta+\\vartheta^{2} \\cdot \\mathrm{dm}\\right)<\/span> \u2026\u00a0 \u2026\u00a0 \u00a0\u00a0 [8.43]<\/p>\n

\u098f\u0996\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (8.40) \u098f\u09ac\u0982 (8.43) \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n\\begin{array}{l}\n\n\\mathrm{dm} c^{2}=\\mathrm{dE}_{\\mathrm{k}} \\\\\n\n\\text { \u09ac\u09be,} \\mathrm{d} \\mathrm{E}_{\\mathrm{k}}=\\mathrm{dm} c^{2}\n\n\\end{array}<\/span>\n

\u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4 \u09b9\u09af\u09bc \u09af\u09c7 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09ad\u09b0\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \\mathrm{dE}_{\\mathrm{k}} \\propto \\mathrm{dm}<\/span><\/span><\/p>\n

\u09ac\u09b8\u09cd\u09a4\u09c1 \u09af\u09a6\u09bf \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09c7, \u09a4\u09ac\u09c7 <\/span> \\vartheta=0<\/span> \u098f\u09ac\u0982, K.E. = 0<\/span><\/p>\n

\u098f\u09ae\u09a4\u09be\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc m = m_0<\/span><\/span>\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 \u09af\u0996\u09a8 <\/span> \u09b9\u09af\u09bc, \u09a4\u0996\u09a8 \u09ad\u09b0\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b9\u09af\u09bc m<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (8.44)-\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987<\/span><\/p>\n\\begin{array}{l}\n\n\\int_{0}^{\\mathrm{E}_{\\mathrm{k}}} \\mathrm{dE}_{\\mathrm{k}}=\\int_{m_{0}}^{\\mathrm{m}} \\mathrm{dm} \\times C^{2} \\\\\n\n\\text { \u09ac\u09be, } E_{k}=\\mathrm{c}^{2} \\int_{m_{0}}^{\\mathrm{m}} \\mathrm{dm} \\\\\n\n\\text { \u09ac\u09be,} E_{k}=\\mathrm{c}^{2}\\left[m-m_{0}\\right] \\\\\n\n\\text { \u09ac\u09be,} E_{k}=m \\mathrm{c}^{2}-m_{0} \\mathrm{c}^{2}\n\n\\end{array}\n\n<\/span>\n

\u098f\u099f\u09bf\u0987 \u09b9\u09b2\u09cb \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964<\/span><\/p>\n

\u09ac\u09b8\u09cd\u09a4\u09c1 \u09af\u09a6\u09bf \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09c7, \u09b9\u09ac\u09c7 \u09a4\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09af\u09c7 \u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09a5\u09be\u0995\u09c7, \u09a4\u09be\u0995\u09c7 <\/span>\u09b8\u09cd\u09a5\u09bf\u09b0 \u09ad\u09b0 \u09b6\u0995\u09cd\u09a4\u09bf <\/b>(Rest mass energy) \u09ac\u09b2\u09c7 \u098f\u09ac\u0982 \u098f\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 =\\mathrm{m}_{0} \\mathrm{c}^{2}<\/span><\/span><\/p>\n

\u2234<\/span> \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ae\u09cb\u099f \u09b6\u0995\u09cd\u09a4\u09bf<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\\mathrm{E}=<\/span>= \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf + \u09b8\u09cd\u09a5\u09bf\u09b0 \u09ad\u09b0 \u09b6\u0995\u09cd\u09a4\u09bf<\/span><\/p>\n

\u09ac\u09be, \\mathrm{E}=\\mathrm{E}_{\\mathrm{k}}+m_{0} \\mathrm{c}^{2}<\/span><\/span><\/p>\n

\u09ac\u09be, \\mathrm{E}=m \\mathrm{c}^{2}-m_{0} \\mathrm{c}^{2}+m_{0} \\mathrm{c}^{2}<\/span><\/span><\/p>\n

\u09ac\u09be, \\mathrm{E}=m \\mathrm{c}^{2}<\/span><\/span>\u00a0 \u00a0<\/span><\/p>\n

\u098f\u099f\u09bf\u0987 \u09b9\u09b2\u09cb \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u0986\u0987\u09a8\u09b8\u09cd\u099f\u09be\u0987\u09a8-\u098f\u09b0 \u09ad\u09b0-\u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964<\/strong><\/p>\n

\u09b8\u09cd\u09a5\u09bf\u09b0 \u09ad\u09b0 (<\/b>Rest mass<\/b>)<\/b><\/h3>\n

\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u0997\u09a4\u09bf\u09ac\u09c7\u0997 \u0986\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u0995\u09be\u099b\u09be\u0995\u09be\u099b\u09bf \u09b9\u09b2\u09c7 \u09ad\u09b0 \u0989\u09b2\u09cd\u09b2\u09c7\u0996\u09af\u09cb\u0997\u09cd\u09af\u09ad\u09be\u09ac\u09c7 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09af\u09bc\u0964 \u098f\u099c\u09a8\u09cd\u09af\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a8\u09bf\u099c\u09b8\u09cd\u09ac \u09a7\u09b0\u09cd\u09ae \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09ad\u09b0\u09c7\u09b0\u00a0 \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09df \u09a4\u09be\u09b0 \u09ad\u09b0 \u09a8\u09bf\u09a4\u09c7 \u09b9\u09af\u09bc\u0964 \u098f\u0995\u09c7\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09ad\u09b0 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09ad\u09b0\u0987 \u09b9\u09b2\u09cb \u098f\u09b0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09ad\u09b0\u0964<\/span><\/p>\n

\u09aa\u09be\u09b0\u09ae\u09be\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0 \u098f\u0995\u0995 (<\/b>Atomic mass unit or amu<\/b>)<\/b><\/h2>\n

\u098f\u0995\u099f\u09bf \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09ad\u09b0 \u0996\u09c1\u09ac\u0987 \u09a8\u0997\u09a3\u09cd\u09af\u0964 \u09a4\u09be\u0987 \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09ad\u09b0 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a8\u09be\u0964 \u09a8\u09bf\u0989\u0995\u09cd\u09b2\u09c0\u09af\u09bc \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u09ad\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u099a\u09b2\u09bf\u09a4 \u098f\u0995\u0995 \u09b9\u09b2\u09cb \u09aa\u09be\u09b0\u09ae\u09be\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0 \u098f\u0995\u0995 (amu)\u0964 1960 \u09b8\u09be\u09b2 \u09a5\u09c7\u0995\u09c7 { }_{6} \\mathrm{C}^{12}<\/span><\/span>\u00a0\u09ae\u09cc\u09b2\u0995\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u09ae\u09cc\u09b2 \u09a7\u09b0\u09c7 \u098f\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0985\u09a8\u09cd\u09af \u09b8\u0995\u09b2 \u09ae\u09cc\u09b2\u09c7\u09b0 \u09ad\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\u098f\u0995 \u09aa\u09be\u09b0\u09ae\u09be\u09a3\u09ac\u09bf\u0995 \u09ad\u09b0 (1 amu) \u09ac\u09b2\u09a4\u09c7 { }_{6} \\mathrm{C}^{12}<\/span><\/span> \u09aa\u09b0\u09ae\u09be\u09a3\u09c1\u09b0 \u09ad\u09b0\u09c7\u09b0 1\/12<\/span>\u00a0\u0985\u0982\u09b6 \u09ac\u09c1\u099d\u09be\u09af\u09bc\u0964<\/span><\/p>\n

1 amu = 1.66057 \\times 10^{-27 \\mathrm{~kg}}<\/span><\/span><\/p>\n

\u09a8\u09bf\u0989\u099f\u09cd\u09b0\u09a8, \u09aa\u09cd\u09b0\u09cb\u099f\u09a8 \u09aa\u09cd\u09b0\u09ad\u09c3\u09a4\u09bf \u0995\u09a3\u09be\u09b0 \u09ad\u09b0 amu \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u098f\u0987 \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u09cb\u099f\u09a8 \u0993 \u09a8\u09bf\u0989\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09ad\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 1.007277 amu \u0993 1.008665 amu<\/span><\/p>\n\\begin{aligned}\n\n1 \\text { amu } \\text { \u09ad\u09b0\u09c7\u09b0 } \\text { \u09b8\u09ae\u09a4\u09c1\u09b2\u09cd\u09af \u09b6\u0995\u09cd\u09a4\u09bf } &=\\frac{1.66377 \\times 10^{-{ }^{27}}\\left(2.998 \\times 10^{8}\\right)^{2}}{1.6022 \\times 10^{19}} \\\\\n\n&=933.3 \\times 10^{6} \\mathrm{eV} \\\\\n\n& \\approx 933 \\mathrm{MeV}\n\n\\end{aligned}<\/span>\n

    \n
  • \u098f\u0995\u099f\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u09ad\u09b0 9.028 \\times 10^{-31} \\mathrm{~kg}<\/span><\/b>\u0964 \u098f\u09b0 \u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09ae\u09a4\u09c1\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u0964 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 \u09ad\u09cb\u09b2\u09cd\u099f (eV)-\u098f \u09ae\u09be\u09a8 \u0995\u09a4 \u09b9\u09ac\u09c7?<\/b><\/li>\n<\/ul>\n

    \u098f\u0996\u09be\u09a8\u09c7,<\/span><\/p>\n\\mathrm{m}_{0}=9.028 10^{-31}kg<\/span>\nc = 3 \\times 10^{8}\u00a0 ms^{-1}<\/span>\n

    \u09a7\u09b0\u09bf, \u09b8\u09ae\u09a4\u09c1\u09b2\u09cd\u09af \u09b6\u0995\u09cd\u09a4\u09bf = E<\/span><\/p>\n

    \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n\\mathrm{E}=\\mathrm{m}_{0} \\mathrm{c}^{2}<\/span>\n

    \u2234<\/span> \u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u09ae\u09a4\u09c1\u09b2\u09cd\u09af, \\begin{aligned}\n\n\\mathrm{E} &=9.028 \\times 10^{-31} \\mathrm{~kg} \\times\\left(3 \\times 10^{8} \\mathrm{~ms}^{-1}\\right)^{2} \\\\\n\n&=8.125 \\times 10^{-14} \\mathrm{~J} \\\\\n\n&=\\frac{8.125 \\times 10{ }^{-14}}{1.6 \\times 10{ }^{19}} \\mathrm{eV} \\\\\n\n&=5.078 \\times 10^{5} \\mathrm{eV} \\\\\n\n&=0.5078 \\mathrm{MeV}\n\n\\end{aligned}<\/span><\/span><\/p>\n

      \n
    • \u098f\u0995\u099f\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 (\u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u09ad\u09b0 \\left.9.1 \\times 10^{-31} \\mathrm{~kg}\\right)<\/span><\/b>) \u0986\u09b2\u09cb\u09b0 \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09b0 90% \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09a4\u09c7 \u099a\u09b2\u099b\u09c7\u0964 \u0986\u0987\u09a8\u09b8\u09cd\u099f\u09be\u0987\u09a8\u09c7\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8\u09c7\u09b0 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u0964<\/b><\/li>\n<\/ul>\n

      \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/span><\/p>\n\\mathrm{m}=\\frac{m_{0}}{\\sqrt{1-v^{2} \/ c^{2}}}<\/span>\n

      \u00a0 \u00a0 \u00a0=\\frac{9.1 \\times 10^{-{ }^{31}}}{\\sqrt{1-\\left(\\frac{0.9 c}{c}\\right)^{2}}}<\/span><\/span><\/p>\n

      \u00a0 \u00a0 \u00a0=2.09 \\times 10^{-30} \\mathrm{kg}<\/span><\/span><\/p>\n

      \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf, \\begin{aligned}\n\n\\mathrm{E}_{\\mathrm{k}}=&\\left(\\mathrm{m}-\\mathrm{m}_{0}\\right) \\mathrm{c}^{2} \\\\\n\n&=\\left(2.09 \\times 10^{-30}-9.1 \\times 10^{-31}\\right) \\times\\left(3 \\times 10^{8}\\right)^{2} \\\\\n\n&=1.062 \\times 10^{-13} \\mathrm{~J}\n\n\\end{aligned}<\/span><\/span><\/p>\n