The ratio of the velocity of light and the velocity of electron in the first orbit of a hydrogen atom. [Given h = 6.624 × 10-27 erg-sec; m = 9.108 × 10-28 g,r = 0.529 × 10-8 cm.]

Question

The ratio of the velocity of light and the velocity of electron in the first orbit of a hydrogen atom. [Given h = 6.624 × 10-27 erg-sec; m = 9.108 × 10-28 g,r = 0.529 × 10-8 cm.] (A) 137 (B) (1/137) (C) (1/13700) (D) 13700

Tardigrade Admin · Accepted Answer

v=(h/2π m) =(6.624 ×10-27/2×3.14×9.108×10-28×0.529×10-8) =2.189 ×108 (e/v)=(3×108/2.189×108)=137

Q. The ratio of the velocity of light and the velocity of electron in the first orbit of a hydrogen atom. [Given $h = 6.624 \times 1 0^{- 27}$ erg-sec; m = $9.108 \times 1 0^{- 28}$ $g, r = 0.529 \times 1 0^{- 8} c m$ .]

$137$

$\frac{1}{137}$

$\frac{1}{13700}$

$13700$

$v = \frac{h}{2 πm}$
$= \frac{6.624 \times 1 0 ^{- 27}}{2 \times 3.14 \times 9.108 \times 1 0 ^{- 28} \times 0.529 \times 1 0 ^{- 8}}$
$= 2.189 \times 1 0^{8}$
$\frac{e}{v} = \frac{3 \times 1 0 ^{8}}{2.189 \times 1 0 ^{8}} = 137$

Q. The ratio of the velocity of light and the velocity of electron in the first orbit of a hydrogen atom. [Given h=6.624×10−27 erg-sec; m = 9.108×10−28 g,r=0.529×10−8cm.]

137

1371​

137001​

13700