Question

A metal of work function 2.3 eV is irradiated with radiation of wavelength \( y \times 10^2 \) nm. The maximum kinetic energy of ejected electron is \( 2.8 \times 10^{-20} \) J. Then calculate \( y \) (in nearest integer).

Hint:

In the photoelectric effect, the energy of the ejected electron is the difference between the energy of the incident photon and the work function of the material.

Answer 1

Correct Answer: 5

Step 1: Apply the photoelectric equation.
According to the photoelectric effect, the energy of the incident photon is used to overcome the work function of the metal and provide kinetic energy to the emitted electron. The relation is: \[ E_{\text{photon}} = \text{Work Function} + \text{Maximum Kinetic Energy} \] The energy of a photon is given by: \[ E_{\text{photon}} = \frac{h c}{\lambda} \] where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the incident radiation.
Step 2: Convert the work function into joules.
Given: \[ \text{Work Function} = 2.3 \, \text{eV} \] Using the conversion \( 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \): \[ \text{Work Function} = 2.3 \times 1.602 \times 10^{-19} \] \[ \text{Work Function} = 3.68 \times 10^{-19} \, \text{J} \]
Step 3: Determine the total photon energy.
The maximum kinetic energy of the emitted electron is: \[ KE = 2.8 \times 10^{-20} \, \text{J} \] Therefore, the total energy of the photon is: \[ E_{\text{photon}} = 3.68 \times 10^{-19} + 2.8 \times 10^{-20} \] \[ E_{\text{photon}} = 3.96 \times 10^{-19} \, \text{J} \]
Step 4: Calculate the wavelength of the radiation.
Using the relation: \[ \lambda = \frac{h c}{E_{\text{photon}}} \] Substituting the known values: \[ \lambda = \frac{(6.626 \times 10^{-34}) (3 \times 10^8)}{3.96 \times 10^{-19}} \] \[ \lambda \approx 5.0 \times 10^{-7} \, \text{m} \] \[ \lambda = 500 \, \text{nm} \]
Step 5: Conclusion.
Hence, the wavelength of the incident radiation is approximately \( 500 \, \text{nm} \). Therefore, \[ y = 5 \]
Final Answer: \( y = 5 \).