A metal surface inside a vacuum cell is illuminated by incident photons each having an ene… — JAMB UTME

A metal surface inside a vacuum cell is illuminated by incident photons each having an energy of $6.2\text{ eV}$ . If the maximum kinetic energy of the emitted photoelectrons is $2.4\text{ eV}$ , what is the work function of the metal in electron-volts ( $\text{eV}$ )?

Answer: 3.8 eV

Answer

The work function of the metal is

3.8\text{ eV}

According to Einstein's photoelectric equation, the total energy of an incident photon (

E = 6.2\text{ eV}

) equals the work function of the metal (

W_0

) plus the maximum kinetic energy of the ejected photoelectrons (

K_{\max} = 2.4\text{ eV}

). Subtracting the kinetic energy from the photon energy gives

W_0 = 6.2\text{ eV} - 2.4\text{ eV} = 3.8\text{ eV}

Step-by-Step Solution

State Einstein's photoelectric equation

E = W_0 + K_{\max}

Relates the incident photon energy to the metal work function and photoelectron kinetic energy.

Rearrange the equation to solve for the work function

W_0 = E - K_{\max}

Isolates the work function

W_0

on one side of the equation.

Substitute the given numerical values and compute

W_0 = 6.2\text{ eV} - 2.4\text{ eV} = 3.8\text{ eV}

Evaluates the difference to obtain the minimum energy needed to remove an electron.

Key Concept

Einstein's Photoelectric Equation and Work Function

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