The wavelength of a violet radiation is `3.7xx10^(5)` pm. What is its frequency ?

Explanation

To find the frequency of the violet radiation given its wavelength, we can follow these steps:

### Step 1: Understand the given information
We are given the wavelength (λ) of violet radiation:
\[ \lambda = 3.7 \times 10^{5} \text{ pm} \]

### Step 2: Convert pico meters to meters
Pico meters (pm) need to be converted to meters (m). We know that:
\[ 1 \text{ pm} = 10^{-12} \text{ m} \]
Thus, we convert the wavelength:
\[ \lambda = 3.7 \times 10^{5} \text{ pm} = 3.7 \times 10^{5} \times 10^{-12} \text{ m} = 3.7 \times 10^{-7} \text{ m} \]

### Step 3: Use the wave equation to find frequency
The wave equation relates the speed of light (C), frequency (ν), and wavelength (λ):
\[ C = \nu \lambda \]
Where:
- \(C\) is the speed of light, approximately \(3 \times 10^{8} \text{ m/s}\)
- \(\nu\) is the frequency in hertz (Hz)
- \(\lambda\) is the wavelength in meters

Rearranging the equation to solve for frequency:
\[ \nu = \frac{C}{\lambda} \]

### Step 4: Substitute the known values
Substituting the values we have:
\[ \nu = \frac{3 \times 10^{8} \text{ m/s}}{3.7 \times 10^{-7} \text{ m}} \]

### Step 5: Calculate the frequency
Now we perform the calculation:
\[ \nu = \frac{3 \times 10^{8}}{3.7 \times 10^{-7}} \approx 0.81 \times 10^{15} \text{ Hz} \]
Thus, the frequency of the violet radiation is:
\[ \nu \approx 8.1 \times 10^{14} \text{ Hz} \]

### Final Answer
The frequency of the violet radiation is approximately \(8.1 \times 10^{14} \text{ Hz}\).

---