Violet light is falling on a photosensitive material causing ejection of photoelectrons with maximum kinetic energy of 1 eV . Red light falling on metal will cause emission of photoelectrons with maximum kinetic energy (approximately) equal to

Options

A. 1.2 eV
B. 0.9 eV
C. 0.5 eV
D. Zero , that is no photoemission

Answer

To solve the problem, we will use the photoelectric effect concept and the photoelectric equation. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect states that when light of sufficient energy (frequency) hits a photosensitive material, it can eject electrons. The maximum kinetic energy (K.E.) of the emitted electrons can be described by the equation:
\[ K.E. = E_{photon} - \phi \]
where \( E_{photon} \) is the energy of the incoming photon and \( \phi \) is the work function of the material.

2. **Given Data**:
- For violet light, the maximum kinetic energy of the emitted photoelectrons is given as 1 eV.
- We need to find the maximum kinetic energy of photoelectrons when red light falls on the same material.

3. **Calculating the Energy of Violet Light**:
- The wavelength of violet light is approximately \( \lambda_1 = 410 \) nm.
- The energy of a photon is given by:
\[ E_{photon} = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light. Using \( hc \approx 1240 \) eV·nm, we can calculate:
\[ E_{photon, violet} = \frac{1240 \text{ eV·nm}}{410 \text{ nm}} \approx 3.02 \text{ eV} \]

4. **Finding the Work Function**:
- Using the photoelectric equation:
\[ K.E. = E_{photon} - \phi \]
Substituting the values we have:
\[ 1 \text{ eV} = 3.02 \text{ eV} - \phi \]
Rearranging gives:
\[ \phi = 3.02 \text{ eV} - 1 \text{ eV} = 2.02 \text{ eV} \]

5. **Calculating the Energy of Red Light**:
- The wavelength of red light is approximately \( \lambda_2 = 680 \) nm.
- Calculate the energy of a photon for red light:
\[ E_{photon, red} = \frac{1240 \text{ eV·nm}}{680 \text{ nm}} \approx 1.82 \text{ eV} \]

6. **Comparing with the Work Function**:
- Now we compare the energy of the red light photon with the work function:
\[ E_{photon, red} = 1.82 \text{ eV} < \phi = 2.02 \text{ eV} \]
Since the energy of the red light photon is less than the work function, no photoelectrons will be emitted.

7. **Conclusion**:
- Therefore, the maximum kinetic energy of the photoelectrons emitted when red light falls on the metal is approximately:
\[ K.E. = 0 \text{ eV} \]

### Final Answer:
The maximum kinetic energy of photoelectrons emitted when red light falls on the metal is approximately **0 eV**.