AP Physics 1 Exam Question: Photoelectric Effect

A metal surface with a work function of 3.2 eV is illuminated with photons of varying frequencies.

(a) Calculate the minimum frequency required for a photon to eject an electron from the metal surface.

(b) If a photon with a frequency of 7.2 × 10^14 Hz strikes the metal surface, determine the maximum kinetic energy of the ejected electron.

(c) Explain why increasing the intensity (number of photons per unit area per unit time) of incident light does NOT increase the maximum kinetic energy of ejected electrons.

Answer:

(a) The minimum frequency required to eject an electron from the metal surface can be determined using the equation:

E = hf - Φ

Where:

• E is the energy of the ejected electron
• h is the Planck's constant (= 6.63 × 10^(-34) Joule-seconds)
• f is the frequency of the photon
• Φ is the work function of the metal surface

To find the minimum frequency, the energy of the ejected electron must be zero:

0 = hf - Φ

Rearranging the equation:

f = Φ / h

Substituting the given values:

f = (3.2 eV * 1.6 × 10^(-19) J/eV) / (6.63 × 10^(-34) J·s)

Simplifying:

f ≈ 4.83 × 10^14 Hz

Therefore, the minimum frequency required to eject an electron from the metal surface is approximately 4.83 × 10^14 Hz.

(b) The maximum kinetic energy of the ejected electron can be determined using the equation:

K.E. = hf - Φ

Where all the variables have the same meaning as in part (a).

Substituting the given values:

K.E. = (6.63 × 10^(-34) J·s) * (7.2 × 10^14 Hz) - (3.2 eV * 1.6 × 10^(-19) J/eV)

Simplifying:

K.E. ≈ 4.74 × 10^(-19) J - 5.12 × 10^(-19) J

K.E. ≈ - 3.8 × 10^(-20) J

However, the kinetic energy of an electron cannot be negative. Therefore, the maximum kinetic energy of the ejected electron is zero.

(c) Increasing the intensity of incident light does NOT increase the maximum kinetic energy of ejected electrons because the maximum kinetic energy depends solely on the frequency of the incident photons and the work function of the metal surface.

Increasing the intensity only affects the number of photons incident on the metal surface per unit time, but not the energy of individual photons. Since increasing intensity only increases the number of photons, it does not change the frequency of each photon. Thus, the maximum kinetic energy of ejected electrons remains the same.