Question

The ratio of ionization energy of Bohr's hydrogen atom and Bohr's hydrogen like lithium atom is -

Assume both atoms in ground state.

• A. $1:1$
• B. $1:3$
• C. $1:9$
• D. None of these

Answer 1

The correct option is C $1:9$

The energy of an electron in the ground state is given as -

$E=-13.6Z^2\text{eV}$

$\Rightarrow E_{\text{ionization}}=13.6Z^2\text{eV}$

So,

$\frac{(E_{\text{ionization}}{)}_H}{(E_{\text{ionization}}{)}_{Li}}={\left(\frac{Z_H}{Z_{Li}}\right)}^2={\left(\frac{1}{3}\right)}^2=\frac{1}{9}=1:9$

Hence, option $\left(C\right)$ is the correct answer.