The shorted wavelength of X- rays emitted from an X- rays tube depends on

Options

A. the current in the tube
B. the voltage applied to the tube
C. the nature of the gas in tube
D. the atomic number of the target material

Answer

To solve the question regarding the dependence of the shortest wavelength of X-rays emitted from an X-ray tube, we can break down the solution into clear steps.

### Step-by-Step Solution:

1. **Understanding the Concept**:
The shortest wavelength of X-rays emitted from an X-ray tube is related to the energy of the electrons that are accelerated through a potential difference in the tube.

**Hint**: Recall that the energy of the electrons is crucial for determining the characteristics of the emitted X-rays.

2. **Kinetic Energy of Electrons**:
The kinetic energy (KE) of the electrons can be expressed as:
\[ KE = eV \]
where \( e \) is the charge of the electron and \( V \) is the potential difference applied.

**Hint**: Remember that the kinetic energy is directly proportional to the potential difference.

3. **Energy-Wavelength Relationship**:
The energy of the emitted X-rays is also related to their wavelength (\( \lambda \)) by the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light.

**Hint**: Consider how energy and wavelength are inversely related.

4. **Combining the Equations**:
Setting the kinetic energy equal to the energy of the emitted X-rays gives us:
\[ eV = \frac{hc}{\lambda} \]
Rearranging this equation to solve for the wavelength (\( \lambda \)) gives:
\[ \lambda = \frac{hc}{eV} \]

**Hint**: Notice how the wavelength is inversely proportional to the potential difference.

5. **Conclusion**:
From the relationship derived, we can conclude that the shortest wavelength of X-rays emitted from the tube depends on the potential difference applied to the tube. Therefore, the answer to the question is that the shortest wavelength of X-rays depends on the voltage applied to the tube.

**Final Answer**: The shortest wavelength of X-rays emitted from an X-ray tube depends on the **voltage applied to the tube**.