Question

The ionisation energy for the H - atom is 13.6eV, then the required energy to excite it from the ground state to next higher state will be: (in eV).

• A. $3.4$
• B. $10.2$
• C. $12.1$
• D. $1.5$

Answer 1

The correct option is B $10.2$

Energy of 1st excited $(n=2)$ state$=-13.6\times \frac{Z^2}{n^2}$

Energy of 1st excited $(n=2)$ state $=-13.6\times \frac{1}{4}$

Energy of 1st excited $(n=2)$ state$=-\frac{13.6}{4}=-3.4eV$

$\therefore$ Energy required for excitation, $\Delta E=E_2-E_1=-3.4-(-13.6)=10.2eV$

The correct option is $\left[B\right]$.