Monochromatic light with a photon energy of 4.5\text{ eV} strikes the surface of a sodium … — JAMB UTME

Monochromatic light with a photon energy of $4.5\text{ eV}$ strikes the surface of a sodium plate inside a vacuum tube. If the work function of sodium is $2.1\text{ eV}$ , what is the maximum kinetic energy of the emitted photoelectrons in electron-volts ( $\text{eV}$ )?

Answer: 2.4 eV

Answer

The maximum kinetic energy of the emitted photoelectrons is 2.4 eV.

According to Einstein's photoelectric theory, energy is conserved such that the energy of an incident photon (

E

) is partly used to liberate an electron from the metal surface (work function

W_0

) and the remaining energy appears as the maximum kinetic energy (

K_{\text{max}}

) of the photoelectron. Subtracting

2.1\text{ eV}

from

4.5\text{ eV}

gives

2.4\text{ eV}

Step-by-Step Solution

Identify the given values from the problem statement

Photon energy

E = 4.5\text{ eV}

, Work function

W_0 = 2.1\text{ eV}

Establishing known variables helps determine the correct photoelectric relation to apply.

Apply Einstein's photoelectric equation

K_{\text{max}} = E - W_0

The maximum kinetic energy of photoelectrons equals the excess energy of incident photons after overcoming the work function.

Calculate the value

K_{\text{max}} = 4.5\text{ eV} - 2.1\text{ eV} = 2.4\text{ eV}

Subtracting the work function from the photon energy yields the final numerical answer.

Key Concept

Einstein's Photoelectric Equation and Energy Conservation

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