In an X-ray tube, electrons are liberated by heating filament and are further accelerated to a very high speed by high potential difference. These accelerated electrons are stopped by a metal target and electron's energy is liberated in the form of X-rays. On increasing the applied potential difference

Options

A. the intensity of emitted radiation increases
B. the intensity of emitted radiation decreases
C. the minimum wavelength of emitted radiation increases
D. the minimum wavelength of emitted radiation decreases.

Explanation

To solve the problem regarding the behavior of an X-ray tube when the applied potential difference is increased, let's break it down step by step.

### Step 1: Understanding the X-ray Tube Setup
In an X-ray tube, electrons are emitted from a heated filament (the cathode) through a process called thermionic emission. These electrons are then accelerated towards a metal target (the anode) by a high potential difference (voltage).

**Hint:** Remember that thermionic emission is the process where heat causes electrons to be released from a material.

### Step 2: Energy of Accelerated Electrons
The energy gained by the electrons when they are accelerated through a potential difference \( V \) is given by the formula:
\[ E = eV \]
where \( e \) is the charge of the electron. This energy is converted into kinetic energy as the electrons strike the target.

**Hint:** The energy of the electrons is directly proportional to the potential difference applied across the tube.

### Step 3: Interaction with Target Atoms
When the high-speed electrons collide with the atoms of the target metal, they transfer their energy to the electrons in the target atoms. This can lead to excitation of the target electrons to higher energy states.

**Hint:** Consider how energy transfer occurs during collisions between the accelerated electrons and the target atoms.

### Step 4: Emission of X-rays
After being excited, the electrons in the target atoms will eventually return to their original energy states, releasing energy in the form of electromagnetic radiation (X-rays) during the de-excitation process. The energy of the emitted X-rays is related to the energy lost by the electrons in the target.

**Hint:** The energy of the emitted X-rays corresponds to the difference in energy levels of the electrons in the target atoms.

### Step 5: Relationship Between Energy and Wavelength
The energy of the emitted X-rays can be expressed using the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the emitted radiation.

**Hint:** This equation shows that energy and wavelength are inversely related.

### Step 6: Effect of Increasing Potential Difference
When the potential difference \( V \) is increased, the energy \( E \) of the accelerated electrons also increases. This results in a higher energy transfer to the target electrons, leading to the emission of X-rays with higher energy. Since energy and wavelength are inversely related, an increase in energy will result in a decrease in the wavelength of the emitted X-rays.

**Hint:** Remember that higher energy corresponds to shorter wavelengths in electromagnetic radiation.

### Conclusion
Thus, when the applied potential difference in an X-ray tube is increased, the minimum wavelength of the emitted X-rays decreases.

**Final Answer:** The minimum wavelength of the emitted radiation will decrease.