What will be the wavenumber of yellow radiation having wavelength 240 nm?

Options

A. `1.724xx10^(4)cm^(-1)`
B. `4.16xx10^(6)m^(-1)`
C. `4xx10^(14)Hz`
D. `219.3xx10^(3)cm^(-1)`

Explanation

To find the wavenumber of yellow radiation with a wavelength of 240 nm, we can follow these steps:

### Step 1: Understand the relationship between wavelength and wavenumber
Wavenumber (ν̅) is defined as the number of waves per unit distance and is given by the formula:
\[ \nu̅ = \frac{1}{\lambda} \]
where λ is the wavelength.

### Step 2: Convert the wavelength from nanometers to meters
The given wavelength is 240 nm. To convert nanometers to meters, we use the conversion factor:
\[ 1 \text{ nm} = 10^{-9} \text{ m} \]
Thus,
\[ \lambda = 240 \text{ nm} = 240 \times 10^{-9} \text{ m} \]

### Step 3: Calculate the wavenumber
Now, we can substitute the value of λ into the wavenumber formula:
\[ \nu̅ = \frac{1}{\lambda} = \frac{1}{240 \times 10^{-9} \text{ m}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ \nu̅ = \frac{1}{240 \times 10^{-9}} = \frac{1}{240} \times 10^{9} \text{ m}^{-1} \]
\[ \nu̅ \approx 4.1667 \times 10^{6} \text{ m}^{-1} \]

### Step 5: Round the result
Rounding the result to three significant figures, we get:
\[ \nu̅ \approx 4.17 \times 10^{6} \text{ m}^{-1} \]

### Final Answer
The wavenumber of yellow radiation having a wavelength of 240 nm is approximately:
\[ \nu̅ \approx 4.17 \times 10^{6} \text{ m}^{-1} \]

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