In an X-rays tube, electrons striking a target are brought to rest, causing X-rays to be emitted. In a paricular X-ray tube, the maximum frequency of the emitted continuum X-ray spectrum is `f_(o)`. If the votage across the tube is doubled, the maximum frequency is

Options

A. `f_(o)//2`
B. `f_(o)//sqrt(2)`
C. `f_(o)`
D. `2f_(o)`

Explanation

To solve the problem, we need to understand the relationship between the voltage applied across the X-ray tube, the kinetic energy of the electrons, and the frequency of the emitted X-rays.

### Step-by-Step Solution:

1. **Understanding the Energy of Electrons:**
The kinetic energy (KE) of the electrons when they are accelerated through a voltage \( V \) is given by the equation:
\[ KE = Q \cdot V \]
where \( Q \) is the charge of the electron and \( V \) is the voltage.

2. **Relating Energy to Frequency:**
The energy of the emitted X-rays is also related to their frequency \( f \) by the equation:
\[ KE = h \cdot f \]
where \( h \) is Planck's constant and \( f \) is the frequency of the emitted X-rays.

3. **Setting Up the Initial Condition:**
Initially, when the voltage is \( V \), the maximum frequency of the emitted X-rays is \( f_0 \). Thus, we can write:
\[ Q \cdot V = h \cdot f_0 \]

4. **Doubling the Voltage:**
If the voltage is doubled, i.e., \( V \) becomes \( 2V \), the new kinetic energy of the electrons becomes:
\[ KE' = Q \cdot (2V) = 2 \cdot (Q \cdot V) \]

5. **Relating New Energy to New Frequency:**
The new kinetic energy can also be expressed in terms of the new frequency \( f' \):
\[ KE' = h \cdot f' \]

6. **Equating the Energies:**
Setting the two expressions for kinetic energy equal gives:
\[ 2 \cdot (Q \cdot V) = h \cdot f' \]
Since we know from the initial condition that \( Q \cdot V = h \cdot f_0 \), we can substitute this into the equation:
\[ 2 \cdot (h \cdot f_0) = h \cdot f' \]

7. **Solving for the New Frequency:**
Dividing both sides by \( h \) (assuming \( h \neq 0 \)):
\[ 2 \cdot f_0 = f' \]

8. **Conclusion:**
Therefore, the maximum frequency of the emitted continuum X-ray spectrum when the voltage is doubled is:
\[ f' = 2f_0 \]

### Final Answer:
The maximum frequency of the emitted X-ray spectrum when the voltage is doubled is \( 2f_0 \).

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