Question

The minimum energy required by a hydrogen atom in ground state to emit radiation in Paschen series is nearly:

• A. 13.6 eV
• B. 12.75 eV
• C. 10.75 eV
• D. 1.5 eV

Hint:

For hydrogen atom, use \( E_n = -13.6/n^2 \) eV and calculate energy difference between levels for transitions.

Answer 1

The Correct Option is B

Step 1: Understand Paschen series.
Paschen series corresponds to transitions ending at \( n = 3 \).

Step 2: Minimum energy condition.
Minimum energy is required to excite electron from ground state \( (n=1) \) to \( n=3 \).

Step 3: Use energy level formula.
\[ E_n = -\frac{13.6}{n^2} \, \text{eV} \]

Step 4: Calculate energies.
\[ E_1 = -13.6 \, \text{eV} \]
\[ E_3 = -\frac{13.6}{9} = -1.51 \, \text{eV} \]

Step 5: Find required energy.
\[ \Delta E = E_3 - E_1 \]
\[ \Delta E = (-1.51) - (-13.6) \]
\[ \Delta E = 12.09 \, \text{eV} \]

Step 6: Approximation.
Closest value among options is \( 12.75 \, \text{eV} \).

Step 7: Final conclusion.
\[ \boxed{12.75 \, \text{eV}} \]