Question

Two photons each of energy \(2~\text{eV}\) incident simultaneously on a photosensitive material of work function \(3~\text{eV}\). The maximum kinetic energy of the emitted photoelectrons is

• A. \(0~\text{eV}\)
• B. \(1~\text{eV}\)
• C. \(2~\text{eV}\)
• D. \(3~\text{eV}\)

Hint:

In photoelectric effect, one photon interacts with one electron — multi-photon absorption is not considered in standard photoelectric emission.

Answer 1

The Correct Option is A

According to the photoelectric equation: \[ K.E_{\text{max}} = E_{\text{photon}} - \phi \] Given:
- Energy of each photon = \(2~\text{eV}\)
- Work function \(\phi = 3~\text{eV}\)
Even if two photons arrive simultaneously, photoelectric effect requires single photon interaction per electron. So only \(2~\text{eV}\) is available, which is less than the work function.
Hence, no photoelectrons are emitted, and: \[ K.E_{\text{max}} = 0~\text{eV} \]

Answer 2

Step 1: Understand the photoelectric equation
The energy of the incident photon must be greater than the work function (\(\phi\)) of the material for electrons to be emitted.
The maximum kinetic energy (\(K_\text{max}\)) of the emitted electron is given by:
\[ K_\text{max} = E_{\text{photon}} - \phi \]

Step 2: Analyze the given values
- Energy of each photon = 2 eV
- Work function \(\phi = 3\) eV

Step 3: Consider simultaneous incidence of two photons
If two photons hit simultaneously, their energies do not combine in the classical photoelectric effect.
Photoelectrons are emitted by absorption of a single photon, so energy per electron is 2 eV.

Step 4: Check if energy is sufficient to emit electrons
Since \(E_{\text{photon}} = 2 \text{ eV} < \phi = 3 \text{ eV}\),
single photons cannot emit photoelectrons as their energy is less than the work function.

Step 5: Calculate maximum kinetic energy
No electrons are emitted, so:
\[ K_\text{max} = 0 \text{ eV} \]

Step 6: Final Conclusion
The maximum kinetic energy of emitted photoelectrons is 0 eV because the photon energy is insufficient to overcome the work function.