An x-ray generator produces photons with energy 49 600 eV or less. Which one of the following phrases most accurately describes the wavelength of these photons?

Options

A. 0.025 nm or longer
B. 0.75 nm or longer
C. 0.050 nm or longer
D. 0.25 nm or shorter

Answer

To solve the problem, we need to determine the wavelength of the X-ray photons produced by the generator, given that their energy is 49,600 eV or less. We can use the relationship between energy and wavelength for photons.

### Step-by-Step Solution:

1. **Understand the Relationship**: The energy (E) of a photon is related to its wavelength (λ) by the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy in electron volts (eV),
- \(h\) is Planck's constant (\(4.135667696 \times 10^{-15} \, \text{eV s}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

2. **Convert the Formula**: We can rearrange the formula to express wavelength in terms of energy:
\[ \lambda = \frac{hc}{E} \]
To make calculations easier, we can use a simplified version that gives wavelength in nanometers when energy is in electron volts:
\[ \lambda (\text{nm}) = \frac{1240}{E (\text{eV})} \]

3. **Substitute the Maximum Energy**: Since the energy of the photons is 49,600 eV or less, we will use this value:
\[ \lambda = \frac{1240}{49600} \]

4. **Calculate the Wavelength**:
\[ \lambda = \frac{1240}{49600} \approx 0.025 \, \text{nm} \]

5. **Interpret the Result**: Since the energy can be less than or equal to 49,600 eV, the wavelength can be greater than or equal to 0.025 nm. Therefore, we can conclude:
\[ \lambda \geq 0.025 \, \text{nm} \]

6. **Select the Correct Phrase**: The phrase that most accurately describes the wavelength of these photons is that the wavelength is "greater than or equal to 0.025 nm".

### Final Answer:
The wavelength of these photons is greater than or equal to 0.025 nm.