Question

If the energy of incident radiation is increased by $25\%$, the kinetic energy of the photoelectrons emitted increases from 0.6 eV to 0.9 eV. The work function of the metal is:

• A. 0.6 eV
• B. 1.2 eV
• C. 1.5 eV
• D. 1 eV

Answer 1

The Correct Option is A

The photoelectric effect can be described using the equation: \( KE = hf - \phi \), where \( KE \) is the kinetic energy of the photoelectrons, \( hf \) is the energy of the incident photons, and \( \phi \) is the work function of the metal. Initially, we have the kinetic energy: \( KE_1 = 0.6 \, \text{eV} \). When the energy of incident radiation increases by 25%, the new energy becomes \( hf_2 = 1.25hf_1 \).
Correspondingly, the kinetic energy increases to \( KE_2 = 0.9 \, \text{eV} \).

Using the equation for the photoelectric effect in both scenarios, we have: 

1. For the initial condition: \( 0.6 = hf_1 - \phi \)
2. For the increased energy: \( 0.9 = 1.25hf_1 - \phi \)

By solving these equations simultaneously, we can find the work function \( \phi \). Subtract equation 1 from equation 2:

\( (0.9 - 0.6) = (1.25hf_1 - hf_1) \)

Which simplifies to:

\( 0.3 = 0.25hf_1 \)

Solving for \( hf_1 \):

\( hf_1 = \frac{0.3}{0.25} = 1.2 \, \text{eV} \)

Substitute \( hf_1 = 1.2 \, \text{eV} \) back into equation 1:

\( 0.6 = 1.2 - \phi \)

Solve for \( \phi \):

\( \phi = 1.2 - 0.6 = 0.6 \, \text{eV} \)

Thus, the work function of the metal is 0.6 eV.

Answer 2

Given:

• Initial kinetic energy of photoelectrons (K₁) = 0.6 eV

• After 25% increase in incident energy, new kinetic energy (K₂) = 0.9 eV

Solution:

1. Let work function be φ and initial incident energy be E.

From Einstein's photoelectric equation: \[ E = φ + K₁ \] \[ E = φ + 0.6\ \text{eV} \]

2. After 25% increase in incident energy: \[ 1.25E = φ + K₂ \] \[ 1.25E = φ + 0.9\ \text{eV} \]

3. Substitute E from first equation: \[ 1.25(φ + 0.6) = φ + 0.9 \] \[ 1.25φ + 0.75 = φ + 0.9 \]

4. Solve for φ: \[ 1.25φ - φ = 0.9 - 0.75 \] \[ 0.25φ = 0.15 \] \[ φ = \frac{0.15}{0.25} = 0.6\ \text{eV} \]