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(B) The electrostatic potential energy of the electron-proton system is defined as zero when they are at an infinite distance apart.To pull the electr

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$3.4 	imes 1.6 	imes 10^{-19} 	ext{ J}$

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(B) The electrostatic potential energy of the electron-proton system is defined as zero when they are at an infinite distance apart.To pull the electron and proton apart from the state $n = 2$,we must provide energy equal to the binding energy of that state.The energy of an electron in the $n$-th orbit of a Hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$.For $n = 2$,the energy is $E_2 = -\frac{13.6}{2^2} = -\frac{13.6}{4} = -3.4 	ext{ eV}$.The work done $W$ required to move the electron to infinity (where $E_f = 0$) is $W = E_f - E_i = 0 - (-3.4 	ext{ eV}) = 3.4 	ext{ eV}$.Converting this to Joules: $W = 3.4 	imes 1.6 	imes 10^{-19} 	ext{ J}$.

How much work must be done to pull apart the electron and the proton that make up the Hydrogen atom,if the atom is initially in the state with $n = 2$?

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