Calculate frequency of yellow radiation having wavelength `5800A^@`.

Options

A. `5.172xx10^14 s^-1`
B. `174 s^-1`
C. `5.172xx10^12 s^-1`
D. `1.74x 10^14 s^-1`

Answer

To calculate the frequency of yellow radiation with a wavelength of 5800 Å (angstroms), we can follow these steps:

### Step 1: Convert Wavelength from Angstroms to Meters
The wavelength given is in angstroms. We need to convert it to meters for our calculations.

1 angstrom (Å) = \(10^{-10}\) meters.

So,
\[ \text{Wavelength} (\lambda) = 5800 \, \text{Å} = 5800 \times 10^{-10} \, \text{m} = 5.8 \times 10^{-7} \, \text{m} \]

### Step 2: Use the Speed of Light Formula
The frequency (\( \nu \)) can be calculated using the formula:
\[ \nu = \frac{c}{\lambda} \]
where:
- \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \)
- \( \lambda \) is the wavelength in meters.

### Step 3: Substitute Values into the Formula
Now, substitute the values into the formula:
\[ \nu = \frac{3 \times 10^8 \, \text{m/s}}{5.8 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate the Frequency
Now, perform the calculation:
\[ \nu = \frac{3 \times 10^8}{5.8 \times 10^{-7}} \approx 5.172 \times 10^{14} \, \text{s}^{-1} \]

### Step 5: Final Answer
Thus, the frequency of the yellow radiation is approximately:
\[ \nu \approx 5.172 \times 10^{14} \, \text{Hz} \]

### Summary
The frequency of yellow radiation with a wavelength of 5800 Å is \( 5.172 \times 10^{14} \, \text{Hz} \).

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