Question

If an $e^{-}$ is revolving in the first bohr orbit of a H atom with a velocity of $2.19 \times 10^8 \, cms^{-1}$, what will be the velocity of the e- in the third orbit of H atom

• A. $2.19 \times 10^8 \, cms^{-1}$
• B. $ 7.3 \times 10^7 \, cms^{-1}$
• C. $6.57 \times 10^8 \, cms^{-1}$
• D. $1.09 \times 10^8 \, cms^{-1}$

Answer 1

Answer: (B)

The velocity of electron in different orbits is given by the following expression:

$V _{ n }= V _{ o } \times \frac{ Z }{ n }$

Given, for first Bohr orbital of $H$ -atom

$V_{0}=2.19 \times 10^{8} cm s ^{-1}$

$\therefore $ The velocity of $e ^{-}$ in third orbit of $H$ -atom is $(\because n =3)$

or $V _{ n } =2.19 \times 10^{8} \times \frac{1}{3}$

$V _{ n } =0.73 \times 10^{8}\, cm\, s ^{-1}$

or $=7.3 \times 10^{7}\, cm\, s ^{-1}$