An X-ray tube is operated at `6.6 kV`. In the continuous spectrum of the emitted X-rays, which of the following frequency will be missing?

Options

A. `10^(18) Hz`
B. `1.5 xx 10^(18) Hz`
C. `2 xx 10^(18) Hz`
D. `2.5 xx 10^(18) Hz`

Explanation

To solve the problem of determining which frequency will be missing from the continuous spectrum of emitted X-rays when an X-ray tube is operated at 6.6 kV, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between energy and frequency**:
The energy (E) of a photon is related to its frequency (ν) by the equation:
\[ E = hν \]
where \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)).

2. **Determine the maximum energy from the voltage**:
The maximum kinetic energy (E) of the electrons in the X-ray tube is given by:
\[ E = eV \]
where \(e\) is the charge of an electron (\(1.6 \times 10^{-19} \, \text{C}\)) and \(V\) is the voltage (6.6 kV = \(6.6 \times 10^3 \, \text{V}\)).

3. **Calculate the maximum energy**:
Substituting the values into the equation:
\[ E = (1.6 \times 10^{-19} \, \text{C})(6.6 \times 10^3 \, \text{V}) = 1.056 \times 10^{-15} \, \text{J} \]

4. **Calculate the maximum frequency**:
Now, using the energy calculated, we can find the maximum frequency:
\[ ν_{\text{max}} = \frac{E}{h} = \frac{1.056 \times 10^{-15} \, \text{J}}{6.626 \times 10^{-34} \, \text{Js}} \approx 1.6 \times 10^{18} \, \text{Hz} \]

5. **Identify missing frequencies**:
The continuous spectrum of emitted X-rays will not include frequencies higher than the maximum frequency calculated. Therefore, any frequency greater than \(1.6 \times 10^{18} \, \text{Hz}\) will be missing.

6. **Check the options**:
If the options provided include frequencies such as \(2.0 \times 10^{18} \, \text{Hz}\) and \(2.5 \times 10^{18} \, \text{Hz}\), these frequencies are higher than \(1.6 \times 10^{18} \, \text{Hz}\) and will be missing from the spectrum.

### Final Answer:
The frequencies \(2.0 \times 10^{18} \, \text{Hz}\) and \(2.5 \times 10^{18} \, \text{Hz}\) will be missing from the continuous spectrum of emitted X-rays.

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