question_answer

If m is mass of electron, v its velocity, r the radius of stationary circular orbit around a nucleus with charge Ze, then from Bohr's first postulate, the kinetic energy \[K=\frac{1}{2}m{{v}^{2}}\]of the electron in C.G.S. system is equal to  [NCERT 1977]

A)   \[\frac{1}{2}\frac{Z{{e}^{2}}}{r}\] 

B)   \[\frac{1}{2}\frac{Z{{e}^{2}}}{{{r}^{2}}}\]

C)   \[\frac{Z{{e}^{2}}}{r}\]              

D)   \[\frac{Ze}{{{r}^{2}}}\]

Correct Answer: A

Solution :

                   In the revolution of electron, coulomb force provides the necessary centripetal force Þ \[\frac{z{{e}^{2}}}{{{r}^{2}}}=\frac{m{{v}^{2}}}{r}\] Þ \[m{{v}^{2}}=\frac{z{{e}^{2}}}{r}\]                                \ K.E.\[=\frac{1}{2}m{{v}^{2}}=\frac{z{{e}^{2}}}{2r}\]