The minimum energy required to cause photoelectric emission when the surface of a metal is irradiated with…

Analyze the question: It asks for the name of the minimum energy needed to free an electron from a metal surface in photoelectric emission.

Explain the concept: In the photoelectric effect, light is made of photons, each with energy E = hf. For an electron to escape from the metal surface, the photon must supply at least a certain minimum energy. This minimum energy is a property of the metal and is called the work function (Φ).

The photoelectric equation is:

hf = Φ + ½mv²max

• hf = energy of the incident photon
• Φ = work function (minimum energy to release an electron)
• ½mv²max = maximum kinetic energy of the emitted electron

At the threshold frequency (f₀), the electron is only just released, with zero kinetic energy:

hf₀ = Φ

Check each option:

• A. Critical energy: Not a standard term in photoelectric emission.
• B. Ionization energy: This is the energy needed to remove an electron from a free atom (gas phase), not from a metal surface.
• C. Work function: This is the minimum energy needed to liberate an electron from a metal surface. ✔
• D. Planck's constant: This is a constant (6.63 × 10⁻³⁴ J s) that relates photon energy to frequency. It is not an energy.

Answer: The correct option is C. work function.

Exam tip: Remember "work function = the work the photon must do to pull the electron out of the metal." Don't confuse it with ionization energy, which is for isolated atoms. Also, the threshold frequency is f₀ = Φ/h, so a metal with a larger work function needs higher-frequency light.