Question

When a hydrogen sample in ground state is bombarded then what potential is required to accelerate electron so that first Paschen line is emitted :-

• A. 2.55 V
• B. 0.65 V
• C. 12.09 V
• D. 12.75 V

Answer 1

Answer: (D)

12.75 V

Answer 2

The hydrogen atom in the ground state (n=1) needs to be excited to at least the n=4 state to subsequently emit the first Paschen line (n=4 to n=3). The energy required for this excitation is the difference between the n=4 and n=1 energy levels: $\Delta E = E_4 - E_1 = (-0.85 \, \text{eV}) - (-13.6 \, \text{eV}) = 12.75 \, \text{eV}$. The accelerating potential required for an electron to impart this energy is numerically equal to this energy in Volts, hence 12.75 V.