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)

$v \propto \frac{1}{n}$

Answer 2

$\because$ 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
$v \propto \frac{1}{n}$