Calculate the wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule. The Cl- Cl bond energy is 243 kJ `mol^(-1) (h=6.6 xx10^(-34)Js,c=3xx10^8m//s, ` Avogadro's number `=6.02xx10^(23)mol^(-1)` )

Options

A. `8.18xx10^(-31)m `
B. `6.26xx10^(-21)m `
C. `4.905xx10^(-7)m `
D. `4.1xx10^(-6)m `

Answer

To calculate the wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule, we will follow these steps:

### Step 1: Convert bond energy from kJ/mol to J
The bond energy of Cl-Cl is given as 243 kJ/mol. We need to convert this to joules.

\[ \text{Energy (E)} = 243 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 243000 \, \text{J/mol} \]

### Step 2: Calculate energy per bond
To find the energy required to break one bond, we divide the total energy by Avogadro's number (6.02 x 10²³ mol⁻¹).

\[ E_{\text{per bond}} = \frac{243000 \, \text{J/mol}}{6.02 \times 10^{23} \, \text{mol}^{-1}} \approx 4.03 \times 10^{-19} \, \text{J} \]

### Step 3: Use the energy to find the wavelength
We will use the formula that relates energy and wavelength:

\[ E = \frac{hc}{\lambda} \]

Where:
- \(E\) is the energy per bond,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

Rearranging the formula to solve for \(\lambda\):

\[ \lambda = \frac{hc}{E} \]

### Step 4: Substitute the values into the equation
Now we can substitute the values into the equation:

\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{4.03 \times 10^{-19} \, \text{J}} \]

Calculating this gives:

\[ \lambda \approx \frac{1.9878 \times 10^{-25}}{4.03 \times 10^{-19}} \approx 4.92 \times 10^{-7} \, \text{m} \]

### Step 5: Convert to nanometers
To express the wavelength in nanometers, we multiply by \(10^9\):

\[ \lambda \approx 4.92 \times 10^{-7} \, \text{m} \times 10^9 \, \text{nm/m} \approx 492 \, \text{nm} \]

### Final Answer
The wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule is approximately **492 nm**.

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