CBSE-XI-Physics
47: The Special Theory of Relativity
- #24Find the mass, the kinetic energy and the momentum of an electron moving at 0.8c.Ans : We know,
Rest mass of electron, m0 = 9.1 × 10-31 kg
Velocity of electron, v = 0.8 c
(a) Mass of electron is given by
`` m=\frac{{m}_{0}}{\sqrt{1-{v}^{2}/{c}^{2}}}``
`` \Rightarrow m=\frac{9.1\times {10}^{-31}}{\sqrt{1-0.64{c}^{2}/{c}^{2}}}=\frac{9.1\times {10}^{-31}}{0.6}``
`` \Rightarrow m=15.16\times {10}^{-31}\,\mathrm{\,kg\,}\approx 15.2\times {10}^{-31}\,\mathrm{\,kg\,}``
(b) Kinetic energy of electron = mc2 - m0c2
`` \,\mathrm{\,KE\,}=\left(m-{m}_{0}\right){c}^{2}``
`` =\left(15.2-9.1\right)\times {10}^{-31}\times 9\times {10}^{16}``
`` =5.5\times {10}^{-14}\,\mathrm{\,J\,}``
(c) Momentum of electron, p = mv
`` p=15.2\times {10}^{-31}\times 0.8\times 3\times {10}^{8}``
`` =3.65\times {10}^{22}\,\mathrm{\,kgm\,}/\,\mathrm{\,s\,}``
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