Question

The work function of Cu is 7.66 $\times 10^{-19}$ J. If photons of wavelength 221 nm are made to strike the surface (h = 6.63 $\times 10^{-34}$ Js), the kinetic energy (in J) of the ejected electrons will be

• A. 2.64 $\times 10^{-18}$
• B. 1.32 $\times 10^{-19}$
• C. 2.64 $\times 10^{-19}$
• D. 5.28 $\times 10^{-19}$

Hint:

In the photoelectric effect, the kinetic energy of ejected electrons is the difference between the photon energy and the work function, provided the photon energy exceeds the work function.

Answer 1

The Correct Option is B

Let’s break this down step by step to calculate the kinetic energy of the ejected electrons and determine why option (2) is the correct answer.
Step 1: Understand the photoelectric effect
The kinetic energy $K_{\text{max}}$ of the ejected electrons is given by Einstein’s photoelectric equation:
\[ K_{\text{max}} = E - \phi \]
where:

• $E$ is the energy of the incident photon,
• $\phi$ is the work function of the material.

Step 2: Calculate the energy of the incident photon
The energy of a photon is:
\[ E = \frac{hc}{\lambda} \]

• Planck’s constant, $h = 6.63 \times 10^{-34} \, \text{J s}$
• Speed of light, $c = 3 \times 10^8 \, \text{m/s}$
• Wavelength, $\lambda = 221 \, \text{nm} = 221 \times 10^{-9} \, \text{m}$

\[ E = \frac{(6.63 \times 10^{-34}) \times (3 \times 10^8)}{221 \times 10^{-9}} \]
\[ E \approx 9.00 \times 10^{-19} \, \text{J} \]
Step 3: Calculate the kinetic energy
Work function, $\phi = 7.66 \times 10^{-19} \, \text{J}$.
\[ K_{\text{max}} = (9.00 \times 10^{-19}) - (7.66 \times 10^{-19}) = 1.34 \times 10^{-19} \, \text{J} \]
This is very close to 1.32 $\times 10^{-19}$ J, likely due to rounding.
Step 4: Confirm the correct answer
The calculated kinetic energy is approximately 1.34 $\times 10^{-19}$ J, which matches option (2) 1.32 $\times 10^{-19}$ J, accounting for slight rounding differences.
Thus, the correct answer is (2) 1.32 $\times 10^{-19}$.