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 (a) its ground state and (b) the state with n = 2 ?

The given data is listed below as-

The principal quantum number is used to describe the electron’s state and is the one-four quantum number assigned to each electron in an atom.

The value of the principal quantum number is a natural number.

The energy emitted by the electron of the hydrogen atom by Bohr’s model is expressed as,

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

For, Z = 1 and n = 1 in the ground state

$$\begin{gathered} E=-13.6{\left(\frac{1}{1}\right)}^{2}eV \\ =-13.6eV \end{gathered}$$

Thus, the value of work done to pull apart the electron and the proton when the atom is initially in its ground state is 13.6 eV .

The energy emitted by the electron of the hydrogen atom by Bohr’s model is expressed as,

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

For, z = 1 and n = 2 state the energy is,

$$\begin{gathered} E=-13.6{\left(\frac{1}{2}\right)}^{2}eV \\ =-3.40eV \end{gathered}$$

Hence, the value of work done to pull apart the electron and the proton when the atom is initially in its state when n = 2 is 3.40 eV .