Question

The work function of a photoelectric material is 4.0 eV. Find the wavelength of light for which the stopping potential is 5 volt.

Hint:

The wavelength of light required for the photoelectric effect can be determined by using the photoelectric equation, considering the work function and stopping potential.

Answer 1

Step 1: Use the Photoelectric Equation.
The energy of the incident photons can be related to the work function and stopping potential using the photoelectric equation: \[ E_{\text{photon}} = \phi + eV_s \] Where:
- \( E_{\text{photon}} = \frac{hc}{\lambda} \) is the energy of the photon,
- \( \phi = 4.0 \, \text{eV} \) is the work function,
- \( eV_s = 5 \, \text{eV} \) is the stopping potential,
- \( h = 6.626 \times 10^{-34} \, \text{J·s} \) is Planck's constant,
- \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light,
- \( \lambda \) is the wavelength of light.
Step 2: Rearranging the Equation.
Substitute \( E_{\text{photon}} \) in the equation: \[ \frac{hc}{\lambda} = \phi + eV_s \] \[ \frac{hc}{\lambda} = 4.0 + 5 = 6.5 \, \text{eV} \]
Step 3: Convert eV to Joules.
1 eV = \( 1.6 \times 10^{-19} \, \text{J} \), so: \[ 6.5 \, \text{eV} = 6.5 \times 1.6 \times 10^{-19} \, \text{J} = 1.04 \times 10^{-18} \, \text{J} \]
Step 4: Solving for Wavelength \( \lambda \).
Now, solve for \( \lambda \): \[ \lambda = \frac{hc}{1.04 \times 10^{-18}} \] Substitute the values of \( h \) and \( c \): \[ \lambda = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{1.04 \times 10^{-18}} = 1.91 \times 10^{-7} \, \text{m} = 191 \, \text{nm} \]
Final Answer:
The wavelength of light is \( \boxed{191 \, \text{nm}} \).