Question

How the linear velocity ‘$v$’ of an electron in the Bohr orbit is related to its quantum number ‘$n$’ ?

• A. $v\propto \frac{1}{n}$
• B. $v\propto \frac{1}{n^2}$
• C. $v\propto \frac{1}{\sqrt{n}}$
• D. $v\propto n$

Answer 1

Answer: (A)

$\because$ Linear velocity of an electron in a orbit of $H$ like atom,
$V=218\times 10^6\times \frac{Z}{n}m/s=\frac{c_0}{137}\cdot \frac{Z}{n}$
where, $Z=$ number of protons in nucleus,
$n=$ principal quantum number
and $c_0=$ speed of light in free space,
Thus, we have
$v\propto \frac{1}{n}$