Question

For electron moving in $n$ th orbit of the atom, the angular velocity is proportional to:

• A. $n$
• B. $\frac{1}{n}$
• C. $n^3$
• D. $\frac{1}{n^3}$

Answer 1

Answer: (D)

$\frac{1}{n^3}$

Radius of nth orbit $r_n=0.529n^2$ $A^o$ $⟹r_n\propto n^2$

Velocity of electron in nth orbit $v_n=2.18\times {10}^6\frac{1}{n}$ m/s $⟹v_n\propto \frac{1}{n}$

$\therefore$ Angular velocity $w_n=\frac{v_n}{r_n}\propto \frac{1/n}{n^2}$

$⟹$ $w_n\propto \frac{1}{n^3}$