Question

If work function of a metal is 6.6 eV, find the threshold wavelength. \text{Given} \( h = 6.6 \times 10^{-34} \, \text{J} \cdot \text{s} \).

Hint:

To find the threshold wavelength, use the relation between the work function and wavelength, considering the speed of light and Planck's constant.

Answer 1

Step 1: Use the equation for threshold wavelength.
The threshold wavelength \( \lambda_{\text{th}} \) is related to the work function \( \phi \) by the equation: \[ \phi = \frac{hc}{\lambda_{\text{th}}} \] where:
- \( \phi \) is the work function,
- \( h \) is Planck's constant,
- \( c \) is the speed of light, and
- \( \lambda_{\text{th}} \) is the threshold wavelength.

Step 2: Rearrange the equation to find \( \lambda_{\text{th}} \).
Rearrange the equation to solve for \( \lambda_{\text{th}} \): \[ \lambda_{\text{th}} = \frac{hc}{\phi} \]
Step 3: Substitute the known values.
Substitute \( h = 6.6 \times 10^{-34} \, \text{J} \cdot \text{s} \), \( c = 3 \times 10^8 \, \text{m/s} \), and \( \phi = 6.6 \, \text{eV} = 6.6 \times 1.6 \times 10^{-19} \, \text{J} \): \[ \lambda_{\text{th}} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{6.6 \times 1.6 \times 10^{-19}} = \frac{1.98 \times 10^{-25}}{1.056 \times 10^{-18}} = 1.87 \times 10^{-7} \, \text{m} \] Thus, the threshold wavelength is: \[ \boxed{1.87 \times 10^{-7} \, \text{m} \, \text{or} \, 187 \, \text{nm}} \]