When ultraviolet radiation is incident on a surface , no photoelectrons are emitted If a second beam causes photoelectrons to be ejected, it may consist of

Options

A. Infrared waves
B. X - rays
C. Visible light rays
D. Radio waves

Answer

To solve the problem, we need to understand the photoelectric effect and the relationship between the energy of incident radiation and the work function of the material.

### Step-by-step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect states that when light (or electromagnetic radiation) hits a material, it can eject electrons if the energy of the incoming photons is greater than the work function (ϕ) of the material. The work function is the minimum energy required to remove an electron from the surface of the material.

2. **Given Information**:
- Ultraviolet (UV) radiation is incident on a surface, but no photoelectrons are emitted.
- This implies that the energy of the UV radiation (E = hν) is less than the work function of the material (ϕ). Thus, we can write:
\[ \phi > h\nu \]

3. **Introducing a Second Beam**:
A second beam of radiation is mentioned that causes photoelectrons to be ejected. For photoelectrons to be emitted, the energy of this second beam must be greater than the work function of the material:
\[ h\nu' > \phi \]
where ν' is the frequency of the second beam.

4. **Comparing Frequencies**:
Since the work function (ϕ) is greater than the energy of the UV radiation, we can conclude that the frequency of the second beam (ν') must be higher than that of the UV radiation (ν). This is because higher frequency radiation has higher energy (E = hν).

5. **Identifying Possible Radiation Types**:
In the electromagnetic spectrum, X-rays have a higher frequency than ultraviolet radiation. Therefore, if the second beam is X-rays, it would have sufficient energy to overcome the work function and eject photoelectrons.

6. **Conclusion**:
The second beam that causes photoelectrons to be ejected must consist of X-rays, as they have a frequency greater than that of ultraviolet radiation.

### Final Answer:
The second beam may consist of X-rays.