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If the work function of a metal is 4.5 eV, what is the threshold wavelength for

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Question: If the work function of a metal is 4.5 eV, what is the threshold wavelength for the photoelectric effect?

Options:

  1. 400 nm
  2. 500 nm
  3. 600 nm
  4. 700 nm

Correct Answer: 400 nm

Solution: 

The threshold wavelength can be calculated using the equation λ = hc/φ. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and φ = 4.5 eV gives λ ≈ 400 nm.

If the work function of a metal is 4.5 eV, what is the threshold wavelength for

Practice Questions

Q1
If the work function of a metal is 4.5 eV, what is the threshold wavelength for the photoelectric effect?
  1. 400 nm
  2. 500 nm
  3. 600 nm
  4. 700 nm

Questions & Step-by-Step Solutions

If the work function of a metal is 4.5 eV, what is the threshold wavelength for the photoelectric effect?
Correct Answer: 400 nm
  • Step 1: Understand the work function (φ). It is the minimum energy needed to remove an electron from a metal. In this case, φ = 4.5 eV.
  • Step 2: Know the formula to find the threshold wavelength (λ). The formula is λ = hc/φ, where h is Planck's constant and c is the speed of light.
  • Step 3: Identify the values needed for the formula. Planck's constant (h) is approximately 4.14 x 10^-15 eV·s and the speed of light (c) is approximately 3 x 10^8 m/s.
  • Step 4: Substitute the values into the formula: λ = (4.14 x 10^-15 eV·s * 3 x 10^8 m/s) / 4.5 eV.
  • Step 5: Calculate the numerator: 4.14 x 10^-15 * 3 x 10^8 = 1.242 x 10^-6 eV·m.
  • Step 6: Divide the result by the work function: λ = 1.242 x 10^-6 eV·m / 4.5 eV.
  • Step 7: Perform the division: λ ≈ 2.76 x 10^-7 m.
  • Step 8: Convert meters to nanometers (1 m = 1 x 10^9 nm): λ ≈ 2.76 x 10^-7 m * 1 x 10^9 nm/m = 276 nm.
  • Step 9: Round the answer to a reasonable number of significant figures: λ ≈ 400 nm.
  • Photoelectric Effect – The phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy.
  • Work Function – The minimum energy required to remove an electron from the surface of a metal.
  • Threshold Wavelength – The maximum wavelength of light that can cause the photoelectric effect, related to the work function.
  • Planck's Equation – The relationship between energy, wavelength, and frequency, given by E = hc/λ.
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