# According to the Bohr theory of the hydrogen atom, what is the minimum energy (in J) needed to ionize a hydrogen atom from the n = 2 state?

Nov 4, 2016

Minimum energy needed to ionize an electron from ${2}^{n d}$ Bohr orbit of hydrogen atom is $5.45 \times {10}^{- 19}$ J/atom.
In Joules per atom, minimum energy needed to ionize an electron from ${n}^{t h}$ Bohr orbit of a hydrogen atom is represented by the formula :
${E}_{n} = - \frac{2.18 \times {10}^{- 18}}{n} ^ 2$ J/atom.
Therefore, minimum energy needed to ionize an electron from ${2}^{n d}$ Bohr orbit of hydrogen atom is,
${E}_{2} =$ $- \frac{2.18 \times {10}^{- 18}}{2} ^ 2$ J/atom $= - \frac{2.18 \times {10}^{- 18}}{4}$ J/atom
$\therefore {E}_{2} = - 0.545 \times {10}^{- 18}$ J/atom $= 5.45 \times {10}^{- 19}$ J/atom. (answer).