# What is the minimum energy required to ionize a hydrogen atom in the n= 3 state?

$2.42 x {10}^{- 16} J$
Use the Bohr Energy Equation for ${n}_{i} = 3 \to {n}_{f} = \infty$
$\Delta {E}_{i}$ = -$A \left(\frac{1}{n} _ {f}^{2} - \frac{1}{n} _ {i}^{2}\right)$ = $- 2.18 x {10}^{- 18} J \left(\frac{1}{\infty} ^ 2 - \frac{1}{3} ^ 2\right)$ = $- 2.18 x {10}^{- 18} J \left(0 - 0.111\right) J = 2.42 x {10}^{-} 19 J$