X-rays of `lamda = 1Å` have frequency

Options

A. `3xx10^(8)Hz`
B. `3xx10^(18)Hz`
C. `3xx10^(10)Hz`
D. `3xx10^(15)Hz`

Answer

To find the frequency of X-rays with a wavelength of 1 Å (angstrom), we can use the relationship between the speed of light, frequency, and wavelength. The formula we will use is:

\[ c = \nu \lambda \]

where:
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( \nu \) is the frequency,
- \( \lambda \) is the wavelength.

### Step-by-Step Solution:

1. **Identify the given values:**
- Wavelength \( \lambda = 1 \) Å.
- Speed of light \( c = 3 \times 10^8 \) m/s.

2. **Convert the wavelength from angstroms to meters:**
- 1 Å = \( 1 \times 10^{-10} \) m.
- Therefore, \( \lambda = 1 \times 10^{-10} \) m.

3. **Rearrange the formula to solve for frequency \( \nu \):**
\[ \nu = \frac{c}{\lambda} \]

4. **Substitute the values into the formula:**
\[ \nu = \frac{3 \times 10^8 \text{ m/s}}{1 \times 10^{-10} \text{ m}} \]

5. **Perform the calculation:**
\[ \nu = 3 \times 10^8 \times 10^{10} = 3 \times 10^{18} \text{ Hz} \]

6. **Conclusion:**
- The frequency of the X-rays is \( 3 \times 10^{18} \) Hz.

### Final Answer:
The frequency of X-rays with a wavelength of 1 Å is \( 3 \times 10^{18} \) Hz.