A metal with a work function of 3.0ev is irradiated with ultraviolet light of energy 4.0 ev. The kinetic energy of the ejected electron is

Analyze the question Light of a given energy hits a metal. We want the kinetic energy of the electrons ejected. This is the photoelectric effect.

Concept Einstein's photoelectric equation:

E = φ + KEmax

• E is the photon energy (4.0 eV)
• φ is the work function, the minimum energy needed to free an electron from the metal (3.0 eV)
• KEmax is the maximum kinetic energy of the ejected electron

Part of the photon's energy is used to free the electron from the metal. The rest becomes the electron's kinetic energy.

Solution

KEmax = E − φ KEmax = 4.0 eV − 3.0 eV KEmax = 1.0 eV

Since 4.0 eV is greater than 3.0 eV, the photon has enough energy to eject electrons, so emission does occur.

Answer: The kinetic energy of the ejected electron is 1.0 eV, which is option A.

Why the other options are wrong

• B (3.0 eV) is just the work function, not the kinetic energy.
• C (4.0 eV) is the total photon energy, but some of it is spent freeing the electron.
• D (7.0 eV) comes from wrongly adding the two values.

Tip: Remember "Photon = Price + Change." The work function is the price paid to free the electron, and the change left over is the kinetic energy. Always subtract: KE = hf − φ. If the photon energy is less than φ, no electrons are emitted.