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 in cgs system)

Question

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 in cgs system) (A) 2 π h c / e2 (B) e r2 h / 2 π c (C) e2 c / 2 π h (D) 2 π e2 / h c

Tardigrade Admin · Accepted Answer

vn=k (2 π e2/n h) We know that in cgs system k=1 ∴ vn=(2 π e2/n h) ⇒ v1=(2 π e2/h) So (v1/c)=(2 π e2/c h)

Q. 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 in cgs system)

$2 πh c / e^{2}$

$e r^{2} h /2 π c$

$e^{2} c /2 πh$

$2 π e^{2} / h c$

$v_{n} = k \frac{2 π e ^{2}}{nh}$
We know that in cgs system $k = 1$
$∴ v_{n} = \frac{2 π e ^{2}}{nh}$
$\Rightarrow v_{1} = \frac{2 π e ^{2}}{h}$
So $\frac{v _{1}}{c} = \frac{2 π e ^{2}}{c h}$

Q. 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 in cgs system)

2πhc/e2

er2h/2πc

e2c/2πh

2πe2/hc