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Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the material is:

  1. 4.5 × 10^15 Hz
  2. 5 × 10^15 Hz
  3. 1.6 × 10^15 Hz
  4. 2.5 × 10^15 Hz

Correct answer: 1.6 × 10^15 Hz

Solution

The energy of the photon emitted during the transition from the first excited state to the ground state in hydrogen is 10.2 eV. Using the photoelectric equation, the threshold frequency is calculated as \( f_0 = \frac{E - eV_0}{h} \), where \( E = 10.2 \) eV, \( eV_0 = 3.57 \) eV, and \( h = 4.14 \times 10^{-15} \) eV·s. Solving gives \( f_0 = 1.6 \times 10^{15} \) Hz.

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