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If a metal has a work function of 4 eV, what is the minimum wavelength of light

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Question: If a metal has a work function of 4 eV, what is the minimum wavelength of light required to cause the photoelectric effect?

Options:

  1. 310 nm
  2. 620 nm
  3. 1240 nm
  4. 2480 nm

Correct Answer: 310 nm

Solution: 

The minimum wavelength can be calculated using the equation λ = hc/W. Substituting h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 4 eV gives λ = 310 nm.

If a metal has a work function of 4 eV, what is the minimum wavelength of light

Practice Questions

Q1
If a metal has a work function of 4 eV, what is the minimum wavelength of light required to cause the photoelectric effect?
  1. 310 nm
  2. 620 nm
  3. 1240 nm
  4. 2480 nm

Questions & Step-by-Step Solutions

If a metal has a work function of 4 eV, what is the minimum wavelength of light required to cause the photoelectric effect?
  • Step 1: Understand the problem. We need to find the minimum wavelength of light that can cause the photoelectric effect for a metal with a work function of 4 eV.
  • Step 2: Know the formula to use. The formula to find the wavelength (λ) is λ = hc/W, where h is Planck's constant, c is the speed of light, and W is the work function.
  • Step 3: Identify the values needed for the formula. We have: h = 4.14 x 10^-15 eV·s, c = 3 x 10^8 m/s, and W = 4 eV.
  • Step 4: Substitute the values into the formula. Replace h, c, and W in the equation λ = hc/W.
  • Step 5: Calculate the wavelength. Perform the calculation to find λ.
  • Step 6: Convert the result to nanometers if necessary. Since 1 nm = 10^-9 m, convert the wavelength from meters to nanometers.
  • 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.
  • Wavelength and Energy Relationship – The relationship between the energy of a photon and its wavelength, given by the equation E = hc/λ.
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