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What is the maximum wavelength of light that can cause the photoelectric effect

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Question: What is the maximum wavelength of light that can cause the photoelectric effect in a metal with a work function of 2.0 eV?

Options:

  1. 620 nm
  2. 400 nm
  3. 500 nm
  4. 300 nm

Correct Answer: 620 nm

Solution:

The maximum wavelength λ_max can be calculated using λ_max = hc/E, where E = 2.0 eV = 3.2 x 10^-19 J. Thus, λ_max = (6.63 x 10^-34 * 3 x 10^8) / (3.2 x 10^-19) = 620 nm.

What is the maximum wavelength of light that can cause the photoelectric effect

Practice Questions

Q1
What is the maximum wavelength of light that can cause the photoelectric effect in a metal with a work function of 2.0 eV?
  1. 620 nm
  2. 400 nm
  3. 500 nm
  4. 300 nm

Questions & Step-by-Step Solutions

What is the maximum wavelength of light that can cause the photoelectric effect in a metal with a work function of 2.0 eV?
Correct Answer: 620 nm
  • Step 1: Understand the photoelectric effect. It occurs when light hits a metal and causes it to emit electrons.
  • Step 2: Know that each metal has a work function, which is the minimum energy needed to release an electron. In this case, the work function is 2.0 eV.
  • Step 3: Convert the work function from electron volts (eV) to joules (J) because we need to use SI units. Use the conversion: 1 eV = 1.6 x 10^-19 J. So, 2.0 eV = 2.0 * 1.6 x 10^-19 J = 3.2 x 10^-19 J.
  • Step 4: Use the formula for maximum wavelength: λ_max = hc/E, where h is Planck's constant (6.63 x 10^-34 J·s) and c is the speed of light (3 x 10^8 m/s).
  • Step 5: Plug in the values into the formula: λ_max = (6.63 x 10^-34 J·s * 3 x 10^8 m/s) / (3.2 x 10^-19 J).
  • Step 6: Calculate the numerator: 6.63 x 10^-34 * 3 x 10^8 = 1.989 x 10^-25 J·m.
  • Step 7: Now divide the numerator by the energy (3.2 x 10^-19 J): λ_max = 1.989 x 10^-25 J·m / 3.2 x 10^-19 J.
  • Step 8: Perform the division to find λ_max: λ_max = 620 nm (nanometers).
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