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Question: The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is...

The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h and c have their usual meanings) –

A

2phc/e2

B

e2 c/2ph

C

e2 h/2pc

D

e2 /2e0hc

Answer

e2 /2e0hc

Explanation

Solution

v = 2πe2kh(Zn)\frac{2\pi e^{2}k}{h}\left( \frac{Z}{n} \right)

Q Z = 1, n = 1

\ v = 2πe2kh\frac{2\pi e^{2}k}{h} vc=2πe2kch\frac{v}{c} = \frac{2\pi e^{2}k}{ch}

Ž2πe2ch(14πε0)\frac{2\pi e^{2}}{ch}\left( \frac{1}{4\pi\varepsilon_{0}} \right)Ž vc=e22ε0ch\frac{v}{c} = \frac{e^{2}}{2\varepsilon_{0}ch}