The energy of an x-ray photon is 4 kev. Its frequency is nearly

Options

A. `10^(18)` Hz
B. `10^(19)` Hz
C. `10^(17)` Hz
D. `10^(10)` Hz

Answer

To find the frequency of an x-ray photon with an energy of 4 keV, we can use the relationship between energy (E) and frequency (ν) given by the equation:

\[ E = h \nu \]

where:
- \( E \) is the energy in joules,
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{J s} \)),
- \( \nu \) is the frequency in hertz (Hz).

### Step-by-Step Solution:

1. **Convert Energy from keV to Joules**:
The energy of the x-ray photon is given as 4 keV. We need to convert this to joules.
- 1 electron volt (eV) = \( 1.6 \times 10^{-19} \) joules.
- Therefore, \( 4 \, \text{keV} = 4 \times 10^3 \, \text{eV} = 4 \times 10^3 \times 1.6 \times 10^{-19} \, \text{J} \).

\[ E = 4 \times 10^3 \times 1.6 \times 10^{-19} = 6.4 \times 10^{-16} \, \text{J} \]

2. **Use the Energy-Frequency Relationship**:
Now, we can use the equation \( E = h \nu \) to find the frequency \( \nu \).
- Rearranging the equation gives us:

\[ \nu = \frac{E}{h} \]

3. **Substitute the Values**:
Substitute the values of \( E \) and \( h \) into the equation:

\[ \nu = \frac{6.4 \times 10^{-16}}{6.63 \times 10^{-34}} \]

4. **Calculate the Frequency**:
Performing the division:

\[ \nu \approx \frac{6.4}{6.63} \times 10^{18} \approx 0.964 \times 10^{18} \approx 10^{18} \, \text{Hz} \]

(Since \( 0.964 \) is approximately \( 1 \), we can round it to \( 10^{18} \, \text{Hz} \)).

### Conclusion:
The frequency of the x-ray photon is nearly \( 10^{18} \, \text{Hz} \).