Question

The speed of the electron (in $ms ^{-1}$ ) in the third orbit of hydrogen atom is approximately
(mass of electron $=9.1 \times 10^{-31}\, kg$ )

• A. $3.6 \times 10^{5}$
• B. $2.18 \times 10^{6}$
• C. $7.26 \times 10^{5}$
• D. $2.18 \times 10^{5}$

Answer 1

Answer: (C)

Velocity of an electron can be given as follows:

Velocity (speed) $[v]=2.18 \times 10^{6} \cdot \frac{Z}{n}$

where, $Z=$ atomic number

$n=$ number of orbit

For hydrogen atom, $Z=1 $

$\Rightarrow n=3$

Therefore, $v =2.18 \times 10^{6} \cdot \frac{Z}{n}=2.18 \times 10^{6} \times \frac{1}{3} $

$=0.726 \times 10^{6}\, ms ^{-1}$

$v =7.26 \times 10^{5} \,ms ^{-1} $