The threshold wavelength for photoelectric emission from a material is `5500` A.Photoelectrons will be emitted,when this material is illuminated with monochromatic radiation from a
(A) `75W` infra-red lamp ,
(B) `10` Willra-red lamp
(C) 75 W ultra-violet lamp
(D) `10 W` ultra-violet lamp

Options

A. `C only `
B. `B` and `C` only `
C. C and D only
D. `A` and `D` only

Answer

To solve the problem, we need to determine which of the given options will emit photoelectrons from a material with a threshold wavelength of 5500 Å (or 550 nm).

### Step-by-Step Solution:

1. **Understand the Threshold Wavelength**:
The threshold wavelength (λ₀) is the maximum wavelength of light that can cause photoelectric emission. For this material, λ₀ = 5500 Å = 550 nm.

2. **Determine the Wavelength Requirement**:
For photoelectrons to be emitted, the wavelength of the incident light (λ) must be less than the threshold wavelength:
\[ λ < λ₀ \]
This means that we need to find light sources that emit wavelengths shorter than 550 nm.

3. **Identify the Types of Lamps**:
- Infrared lamps emit light with wavelengths longer than 700 nm, which is beyond the threshold wavelength. Thus, they cannot emit photoelectrons.
- Ultraviolet (UV) lamps emit light with wavelengths shorter than 400 nm, which is well below the threshold wavelength.

4. **Evaluate Each Option**:
- **(A) 75 W Infra-red lamp**: Infrared light has wavelengths longer than 700 nm. **(Not suitable)**
- **(B) 10 W Infra-red lamp**: Same reasoning as (A). **(Not suitable)**
- **(C) 75 W Ultra-violet lamp**: UV light has wavelengths shorter than 400 nm. **(Suitable)**
- **(D) 10 W Ultra-violet lamp**: UV light also has wavelengths shorter than 400 nm. **(Suitable)**

5. **Conclusion**:
Both options (C) and (D) can emit photoelectrons. However, since the question asks for monochromatic radiation, we can conclude that both UV lamps are suitable.

### Final Answer:
The correct options are (C) 75 W ultra-violet lamp and (D) 10 W ultra-violet lamp.