The frequency of light ray having the wavelength 3000 Å is

Options

A. `9xx10^(13)` cycles/sec
B. `10^(15)` cycles/sec
C. 90 cycles/sec
D. 3000 cycles/sec

Answer

To find the frequency of a light ray with a wavelength of 3000 Å (angstroms), we can use the formula that relates frequency (ν), speed of light (c), and wavelength (λ):

### Step-by-Step Solution:

1. **Understand the relationship**: The frequency of light is given by the formula:
\[ \nu = \frac{c}{\lambda} \]
where:
- \( \nu \) is the frequency,
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength.

2. **Convert the wavelength from angstroms to meters**:
- 1 angstrom (Å) = \( 10^{-10} \) meters.
- Therefore, \( 3000 \, \text{Å} = 3000 \times 10^{-10} \, \text{m} = 3 \times 10^{-7} \, \text{m} \).

3. **Substitute the values into the frequency formula**:
\[ \nu = \frac{3 \times 10^8 \, \text{m/s}}{3 \times 10^{-7} \, \text{m}} \]

4. **Calculate the frequency**:
- Simplifying the expression:
\[ \nu = \frac{3 \times 10^8}{3 \times 10^{-7}} = 10^{8 - (-7)} = 10^{8 + 7} = 10^{15} \, \text{Hz} \]

5. **Final result**: The frequency of the light ray is:
\[ \nu = 10^{15} \, \text{Hz} \quad \text{or} \quad 10^{15} \, \text{cycles per second} \]

### Summary:
The frequency of the light ray having a wavelength of 3000 Å is \( 10^{15} \, \text{Hz} \).

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