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Photoelectric Effect

A public photoelectric-effect question showing how a photon's energy splits between the work function and the electron's maximum kinetic energy.

Question

Ultraviolet light of wavelength 248 nm248\,\text{nm} (use hc≈1240 eV⋅nmhc \approx 1240\,\text{eV}\cdot\text{nm}) illuminates a metal surface whose work function is ϕ=2.0 eV\phi = 2.0\,\text{eV}. What is the maximum kinetic energy of the ejected photoelectrons?

  1. a.2.0 eV2.0\,\text{eV}
  2. b.3.0 eV3.0\,\text{eV}
  3. c.5.0 eV5.0\,\text{eV}
  4. d.7.0 eV7.0\,\text{eV}

Correct answer

B. 3.0 eV3.0\,\text{eV}

Full reasoning

  1. 1Convert wavelength to photon energy: E=hc/λ=1240 eV⋅nm/248 nm=5.0 eVE = hc/\lambda = 1240\,\text{eV}\cdot\text{nm}/248\,\text{nm} = 5.0\,\text{eV}.
  2. 2Apply the photoelectric equation: Kmax=hf−ϕ=5.0−2.0 eVK_{max} = hf - \phi = 5.0 - 2.0\,\text{eV}.
  3. 3The fastest photoelectrons leave with 3.0 eV3.0\,\text{eV}; a stopping potential of 3.0 V3.0\,\text{V} would just barely halt them.

Why each choice is right or wrong

Choice A

This is the work function itself — the minimum energy needed to free an electron — not the kinetic energy left over afterward.

Choice B

Correct. The photon energy is 1240/248=5.0 eV1240/248 = 5.0\,\text{eV}, and Kmax=5.0−2.0=3.0 eVK_{max} = 5.0 - 2.0 = 3.0\,\text{eV}.

Choice C

This is the full photon energy; it forgets that 2.0 eV2.0\,\text{eV} must be spent freeing the electron from the metal.

Choice D

This adds the work function to the photon energy instead of subtracting it, giving the electron energy it never received.

Related formula

Photoelectric equation

Kmax=hf−ϕK_{\text{max}} = hf - \phi

Assumptions: Each ejected electron absorbs the energy of a single photon.

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Sources

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 3, Section 6.2: Photoelectric Effect — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-08-07

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