Hydrogen-like atom is in an external magnetic field $B=1.6 \ T$.

**a)** What is the energy difference ($\triangle E$) between the successive $m_l$-levels in same $l$-shell of atom? (Give the answer in $eV$.)

**I tried this:**

$E_n = -\frac{13.6 \ eV}{n^2}$

$\triangle E = E_2 - E_1 = -\frac{13.6 \ eV}{2^2} - (-\frac{13.6 \ eV}{1^2}) = -\frac{13.6 \ eV}{4} + 13.6 \ eV =10.2 \ eV$

But I didn't get correct answer. So please help me, how should I get correct answer? Any help is appreciated, thanks in advance!