Photoelectric Effect

1. Understand the Photoelectric Effect

When light of a suitable frequency illuminates a metal surface, electrons are emitted. The maximum kinetic energy of these electrons depends on the frequency of the light and the work function of the metal.

2. Einstein's Photoelectric Equation

Einstein's photoelectric equation relates the energy of the incident photon ( ), the work function of the metal ( ), and the maximum kinetic energy of the emitted electron ( ):

where:

• ( is Planck's constant, and is the frequency of light)
• is the work function
• is the maximum kinetic energy

3. Apply the Equation to Both Cases

For light of frequency Hz:

For light of frequency Hz:

4. Apply the Given Condition

We are given that .

5. Substitute and Solve

Substitute into the first equation:

Subtract the second equation from this:

Simplify:

Substitute from the second equation:

Solve for :

6. Find the Threshold Frequency

The threshold frequency ( ) is the minimum frequency required for photoemission. At this frequency, .

Substitute and into the second equation:

Therefore, the threshold frequency of the metal is Hz.

The correct answer is (4) .

Step 1: Applying Einstein’s Photoelectric Equation The kinetic energy of the emitted photoelectron is: Since kinetic energy is related to momentum as: Equating both expressions:
Step 2: Deriving de Broglie Wavelength From de Broglie’s equation: Solving for : Substituting into the de Broglie equation:
Step 3: Establishing Proportionality Since and are constants: Thus, the correct answer is: