Question

What is the energy in $eV$ required to excite the electron from $n=1$ to $n=2$ state in hydrogen atom? ($n=$ principal quantum number)

• A. $13.6$
• B. $3.4$
• C. $17$
• D. $10.2$

Answer 1

The correct option is D $10.2$

The energy of nth orbit is given by,

$E_n=-\frac{k}{n^2}$ (K $=13.6eV=$ constant)

The energy required to excite an electron from n=1 to n=2 is

$\Delta E_{(2,1)}=E_2-E_1$

$=K[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$

$=13.6eV[\frac{1}{1^2}-\frac{1}{2^2}]\cong 10.2eV$