Question

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

• A. $\frac{2}{3}$
• B. $\frac{4}{9}$
• C. $\frac{8}{27}$
• D. 1

Answer 1

The correct option is C $\frac{8}{27}$

According to bohr's model of an atom
$V_n\propto \frac{Z}{n}$
$r_n\propto \frac{n^2}{Z}$
The acceleration of the electron
$a=\frac{V_z^2}{r_n}\propto \frac{Z^3}{n^4}$
For ground state, n = 1
$a\propto Z^3$
$\frac{a_{He}}{a_{Li}}=\frac{Z_{He}^3}{Z_{Li}^3}=\frac{2^3}{3^3}=\frac{8}{27}$