Question

The ratio between total acceleration of the electron on singly ionized helium atom and hydrogen atom (both in ground state) is

• A. $1$
• B. $8$
• C. $4$
• D. $16$

Answer 1

Answer: (B)

$8$

As according to Bohr' model of an atom, $v_n=2.18\times {10}^6\frac{Z}{n}\propto \frac{Z}{n}$

Also, $r_n=0.529\frac{n^2}{Z}\propto \frac{n^2}{Z}$

Thus angular acceleration of the electron, $a=\frac{v_n^2}{r_n}\propto \frac{Z^3}{n^4}$

For ground state, i.e, $n=1$ $⟹a\propto Z^3$

$\therefore \frac{a_{He}}{a_H}=\frac{Z_{He}^3}{Z_H^3}=\frac{2^3}{1}=8$