Given the visible green light has a wavelength of `510` nm then corresponding frequency and wave number are respectively `(C = 3xx10^(8)ms^(-1))` :

Options

A. `5.8xx10^(14)Hz, 0.001nm`
B. `6xx10^(16)Hz, 0.004 nm^(-1)`
C. `5.8xx10^(14)Hz, 0.001 nm^(-1)`
D. `5xx10^(12)Hz, 0.008 nm`

Answer

To solve the problem of finding the corresponding frequency and wave number for the visible green light with a wavelength of 510 nm, we will follow these steps:

### Step 1: Convert Wavelength from Nanometers to Meters
The given wavelength (λ) is in nanometers. We need to convert it to meters for our calculations.

\[ \lambda = 510 \, \text{nm} = 510 \times 10^{-9} \, \text{m} \]

### Step 2: Use the Speed of Light to Find Frequency
We can use the formula that relates the speed of light (C), frequency (ν), and wavelength (λ):

\[ \nu = \frac{C}{\lambda} \]

Where:
- \( C = 3 \times 10^8 \, \text{m/s} \)
- \( \lambda = 510 \times 10^{-9} \, \text{m} \)

Substituting the values:

\[ \nu = \frac{3 \times 10^8 \, \text{m/s}}{510 \times 10^{-9} \, \text{m}} \]

Calculating this gives:

\[ \nu \approx 5.88 \times 10^{14} \, \text{Hz} \]

### Step 3: Calculate Wave Number
The wave number (k) is defined as the reciprocal of the wavelength:

\[ k = \frac{1}{\lambda} \]

Using the wavelength in meters:

\[ k = \frac{1}{510 \times 10^{-9} \, \text{m}} \]

Calculating this gives:

\[ k \approx 1.96 \times 10^6 \, \text{m}^{-1} \]

Alternatively, if we want to express this in terms of nanometers:

\[ k = \frac{1}{510 \, \text{nm}} \approx 0.00196 \, \text{nm}^{-1} \]

### Final Answers
Thus, the corresponding frequency and wave number for the visible green light are:

- Frequency (ν) = \( 5.88 \times 10^{14} \, \text{Hz} \)
- Wave number (k) = \( 1.96 \times 10^6 \, \text{m}^{-1} \) or \( 0.00196 \, \text{nm}^{-1} \)

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