The work function of a metal is 2.1 eV. What is the wavelength of light that will just cause the pho

JAMB Physics 2023 85 views

The work function of a metal is 2.1 eV. What is the wavelength of light that will just cause the photoelectric effect in this metal?

[h = 6.63 x 10⁻³⁴ Js; 1 ev = 1.6 x 10⁻¹⁹ J]

  1. 642 nm
  2. 409 nm
  3. 734 nm
  4. 592 nm ✓

Explanation

Step 1: Identify given values and what to find
Given: W = 2.1 eV, h = 6.63 × 10⁻³⁴ Js, c = 3 × 10⁸ ms⁻¹
Find: Threshold wavelength λ₀

Step 2: Convert work function to joules
W = 2.1 × 1.6 × 10⁻¹⁹ = 3.36 × 10⁻¹⁹ J

Step 3: At threshold, photon energy equals work function
Formula: E = hc/λ₀ = W
Therefore: λ₀ = hc/W

Step 4: Substitute and calculate
λ₀ = (6.63 × 10⁻³⁴ × 3 × 10⁸)/(3.36 × 10⁻¹⁹)
λ₀ = (1.989 × 10⁻²⁵)/(3.36 × 10⁻¹⁹)
λ₀ = 5.92 × 10⁻⁷ m = 592 nm

Step 5: The answer is 592 nm

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