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Q. The velocity of electron in first orbit of $H$-atom as compared to the velocity of light is :

BITSATBITSAT 2005

Solution:

Velocity of light $=3 \times 10^{10} cm / sec$.
Velocity of an electron in the orbit is given by the expression,
$v =\frac{ nh }{2 \pi mr }$,
where, $h$ is Planck's constant $=6.6256 \times 10^{-34} Js$.
$m$ is mass of electron $=9.1096 \times 10^{-31} kg$.
$r$ is radius of orbit $=0.529 \times 10^{-10} \times n ^{2} m$.
For $1^{\text {st }}$ orbit of H-atom, $r =0.529 \times 10^{-10} \times 1^{2} m$.
Substituting these values in the expression of velocity, we get v $=2.18 \times 10^{8} cm / sec$.
Comparing the velocity of the first orbit of $H$-atom with the velocity of light, we get to know that velocity of the first orbit of $H$ - atom is $\frac{1}{100}$ th of the velocity of light.