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
The wavenumber (\( \bar{\nu} \)) is defined as the reciprocal of the wavelength (\( \lambda \)). The relationship can be expressed as:
\[ \bar{\nu} = \frac{1}{\lambda} \]
where \( \bar{\nu} \) is in meters inverse (m\(^{-1}\)) when \( \lambda \) is in meters.

### Step 2: Convert the wavelength from nanometers to meters
Given that the wavelength is 240 nm, we need to convert this to meters:
\[ \lambda = 240 \, \text{nm} = 240 \times 10^{-9} \, \text{m} \]

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

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

### Step 5: Convert to centimeters inverse (optional)
If needed, we can convert this to centimeters inverse (cm\(^{-1}\)):
\[ \bar{\nu} = 4.1667 \times 10^{6} \, \text{m}^{-1} = 4.1667 \times 10^{6} \times 100 \, \text{cm}^{-1} = 4.1667 \times 10^{8} \, \text{cm}^{-1} \]

However, if we want to express it in a more manageable form, we can also express it as:
\[ \bar{\nu} \approx 4.16 \times 10^{6} \, \text{m}^{-1} \]

### Final Answer
Thus, the wavenumber of yellow radiation having a wavelength of 240 nm is approximately:
\[ \bar{\nu} \approx 4.16 \times 10^{6} \, \text{m}^{-1} \]

---