Question

The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is

• A. \( 1.37 \times 10^{-7} \, \text{m} \)
• B. \( 1.5 \times 10^{-7} \, \text{m} \)
• C. \( 3.7 \times 10^{-7} \, \text{m} \)
• D. \( 4 \times 10^{-7} \, \text{m} \)

Hint:

The energy of a photon required to initiate the photoelectric effect is the work function of the metal, and this relates to the wavelength using the equation \( E = \frac{hc}{\lambda} \).

Answer 1

The Correct Option is A

The energy of a photon is related to its wavelength \( \lambda \) by: \[ E = \frac{hc}{\lambda} \] Where \( h \) is Planck's constant and \( c \) is the speed of light. The energy required to initiate the photoelectric effect is equal to the work function \( \phi \) of the metal. Given \( \phi = 9 \, \text{eV} \), we convert it to joules: \[ \phi = 9 \times 1.6 \times 10^{-19} \, \text{J} \] Now, solving for \( \lambda \): \[ \lambda = \frac{hc}{\phi} = \frac{(6.63 \times 10^{-34})(3 \times 10^8)}{9 \times 1.6 \times 10^{-19}} = 1.37 \times 10^{-7} \, \text{m} \] Thus, the longest wavelength of light is \( 1.37 \times 10^{-7} \, \text{m} \).