Question

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

• A. $2$
• B. $4/9$
• C. $8/27$
• D. $1$

Answer 1

The correct option is C $8/27$

According Bohr's model of an atom $V_n=2.18\times {10}^{\frac{z}{n}}\propto \frac{z}{n}$

$r_n=0.529\frac{n^2}{z}\propto \frac{n^2}{z}$

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

for ground state $n=1$

$\Rightarrow a\propto z^3$

$\frac{a_{He}}{a_{Li}}=\frac{z_{He}^3}{z_{Li}^3}=\frac{z^3}{3^3}=\frac{8}{27}$

$z_{He}=2$

$z_{Li}=3$.