`lambda_("min")` of X-rays depends on :-

Options

A. Atomic number of target
B. Energy of electron
C. Both (A) & (B)
D. None of these

Answer

To determine what the minimum wavelength (\( \lambda_{\text{min}} \)) of X-rays depends on, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding X-rays**:
- X-rays are a form of highly penetrating electromagnetic radiation, which means they have a shorter wavelength compared to visible light.

2. **Energy of Photons**:
- The energy (\( E \)) of a photon is given by the equation:
\[ E = h \nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the radiation.

3. **Relating Frequency to Wavelength**:
- The frequency (\( \nu \)) can also be expressed in terms of wavelength (\( \lambda \)) and the speed of light (\( c \)):
\[ \nu = \frac{c}{\lambda} \]
- Substituting this into the energy equation gives:
\[ E = \frac{hc}{\lambda} \]

4. **Finding Minimum Wavelength**:
- Rearranging the equation for \( \lambda \) gives us:
\[ \lambda = \frac{hc}{E} \]
- To find the minimum wavelength (\( \lambda_{\text{min}} \)), we note that as the energy (\( E \)) increases, the wavelength (\( \lambda \)) decreases. Therefore, the minimum wavelength is inversely proportional to the energy of the photon.

5. **Conclusion**:
- From the relationship derived, we can conclude that the minimum wavelength of X-rays depends on the energy of the electrons producing the X-rays.

### Final Answer:
The minimum wavelength (\( \lambda_{\text{min}} \)) of X-rays depends on the energy of the electron.