Question

The work function of a given metal is 4 eV. The longest wavelength of light that can cause photoelectron emission from this metal is:

• A. 220 nm
• B. 400 nm
• C. 310 nm
• D. 520 nm

Hint:

In photoelectric effect problems, remember that the work function represents the energy required to release electrons from the metal, and the wavelength of the light is inversely proportional to the energy.

Answer 1

The Correct Option is B

The work function \( W \) is given by the equation: \[ W = \frac{hc}{\lambda} \] where:
- \( W = 4 \, \text{eV} \) is the work function,
- \( h = 6.626 \times 10^{-34} \, \text{J·s} \) is Planck's constant,
- \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light,
- \( \lambda \) is the wavelength of light in meters.
Rearranging the formula to solve for \( \lambda \), we get: \[ \lambda = \frac{hc}{W} \] Substitute the values: \[ \lambda = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{4 \times 1.602 \times 10^{-19}} \approx 400 \, \text{nm} \] Thus, the longest wavelength of light that can cause photoelectron emission is 400 nm.