Question

A radiation of energy 11.0 eV is irradiated on gaseous hydrogen atoms at room temperature. Identify the energy level to which electron of hydrogen atom can be excited:

• A. \(E_5\)
• B. \(E_2\)
• C. \(E_3\)
• D. \(E_4\)

Hint:

Hydrogen excitation depends on exact energy gaps between quantized levels.

Answer 1

The Correct Option is B

Step 1: Hydrogen energy level expression.
E_n = -13.6/n² eV.

Step 2: Ground state value.
E₁ = -13.6 eV.

Step 3: Excitation energy to n=2.
ΔE = 13.6(1 - 1/4) = 10.2 eV.

Step 4: Assessing the supplied photon.
Photon energy = 11.0 eV, sufficient to reach n=2 but not precisely matching higher stable states.

Step 5: Testing n=3.
Required energy for n=3 is 12.09 eV>11.0 eV, so inaccessible.

Step 6: Conclusion.
Thus, the electron is promoted to E₂.