The frequency associated with photon of radiation having a wavelength of 6000 Å is

Options

A. `5 xx 10^(14)` Hz
B. `5 xx 10^(10)` Hz
C. `2 xx 10^(14)` Hz
D. `5 xx 10^(15)` Hz

Answer

To find the frequency associated with a photon of radiation having a wavelength of 6000 Å, we can use the formula that relates the speed of light (c), frequency (f), and wavelength (λ):

\[ c = f \cdot \lambda \]

### Step-by-Step Solution:

1. **Identify the Known Values**:
- Wavelength (λ) = 6000 Å
- Speed of light (c) = \( 3 \times 10^8 \) m/s

2. **Convert Wavelength from Angstroms to Meters**:
- 1 Ångström (Å) = \( 10^{-10} \) meters
- Therefore, \( 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6.0 \times 10^{-7} \, \text{m} \)

3. **Rearrange the Formula to Solve for Frequency (f)**:
- From the equation \( c = f \cdot \lambda \), we can rearrange it to find frequency:
\[ f = \frac{c}{\lambda} \]

4. **Substitute the Known Values into the Formula**:
- Now substitute \( c \) and \( \lambda \) into the rearranged formula:
\[ f = \frac{3 \times 10^8 \, \text{m/s}}{6.0 \times 10^{-7} \, \text{m}} \]

5. **Calculate the Frequency**:
- Performing the division:
\[ f = \frac{3 \times 10^8}{6.0 \times 10^{-7}} \]
\[ f = 0.5 \times 10^{15} \, \text{Hz} \]
- This can also be written as:
\[ f = 5.0 \times 10^{14} \, \text{Hz} \]

### Final Answer:
The frequency associated with the photon of radiation having a wavelength of 6000 Å is \( 5.0 \times 10^{14} \, \text{Hz} \).

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