One of the following wavelength is absent and the rest are present in the X-rays coming from a Coolidge tube. Which one is the absent wavelength?

Options

A. 25 pm
B. 50 pm
C. 75 pm
D. 100 pm

Answer

To determine which wavelength is absent in the X-rays produced by a Coolidge tube, we need to analyze the options given and apply our understanding of X-ray production.

### Step-by-Step Solution:

1. **Understanding the Coolidge Tube**:
- A Coolidge tube is a type of X-ray tube that operates under high vacuum conditions. It uses a heated filament to produce electrons, which are then accelerated towards a target to produce X-rays.
- The production of X-rays involves the interaction of high-energy electrons with the target material.

2. **Cut-off Wavelength**:
- The cut-off wavelength (λ_c) is the maximum wavelength of X-rays that can be produced by the tube. It is determined by the maximum energy of the electrons striking the target.
- The relationship between the cut-off wavelength and the maximum energy (E) of the electrons is given by the formula:
\[ λ_c = \frac{hc}{E} \]
- Where \( h \) is Planck's constant and \( c \) is the speed of light.

3. **Analyzing the Options**:
- The options provided are:
- 25 picometers
- 50 picometers
- 75 picometers
- 100 picometers
- We know that the cut-off wavelength is greater than 25 picometers. Therefore, wavelengths shorter than 25 picometers can be produced, while those longer than this cut-off may not be present.

4. **Identifying the Absent Wavelength**:
- Since the cut-off wavelength is greater than 25 picometers, this means that the wavelength of 25 picometers cannot be produced by the Coolidge tube.
- The other options (50 picometers, 75 picometers, and 100 picometers) are all greater than 25 picometers and can be produced.

5. **Conclusion**:
- The absent wavelength in the X-rays coming from a Coolidge tube is **25 picometers**.

### Final Answer:
The absent wavelength is **25 picometers**.