Question

For a hydrogen atom, the energy of a stationary electron is given by \( E_n = -\frac{13.6}{n^2} \, \text{eV} \). The energy required to excite the electron to the second excited state and to the ionized state are:

• (a) 10 eV, (b) 13.6 eV
• (a) 12 eV, (b) 13.6 eV
• (a) 8 eV, (b) 10.6 eV
• (a) 8 eV, (b) 13.6 eV

Hint:

Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \) to compute energy levels of hydrogen atom.

Answer 1

The Correct Option is B

Ground state energy = \( E_1 = -13.6 \, \text{eV} \)
Second excited state \( n = 3 \Rightarrow E_3 = -\frac{13.6}{9} = -1.51 \, \text{eV} \)
\[ \text{Energy required for (a)} = E_3 - E_1 = (-1.51) - (-13.6) = 12.09 \approx 12 \, \text{eV} \] \[ \text{Energy required for (b)} = 0 - (-13.6) = 13.6 \, \text{eV} \]