Question 8 of 10intermediate🔧 ApplyNumerical3 marks

Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.

Correct Answer

The work function of the material is 2.17 eV.

Exercise: EXERCISES | Q: 11.9 | (Page 285)
For More Understanding

Explanation

This problem applies Einstein's photoelectric equation. The energy of incident photons is calculated using E = hc/λ, and the maximum kinetic energy of photoelectrons equals eV₀ (where V₀ is stopping potential). The work function is then found by subtracting kinetic energy from photon energy.

Solution Steps

  1. Step 1: Calculate energy of incident photon Using E = hc/λ λ = 488 nm = 488×10488 \times 10⁻⁹ m E = (6.63×106.63 \times 10⁻³⁴ J s × 3×103 \times 10⁸ m/s)/(488×10488 \times 10⁻⁹ m) E = 4.08×104.08 \times 10⁻¹⁹ J Converting to eV: E = (4.08×104.08 \times 10⁻¹⁹)/(1.6×101.6 \times 10⁻¹⁹) = 2.55 eV

  2. Step 2: Calculate maximum kinetic energy of photoelectrons K_max = eV₀ K_max = e × 0.38 V = 0.38 eV

  3. Step 3: Apply Einstein's photoelectric equation Using hν = φ₀ + K_max φ₀ = hν - K_max φ₀ = 2.55 eV - 0.38 eV = 2.17 eV

PreviousNext