The energy required to break one mole of Cl-Cl bonds in `Cl_(2)` is 242 kJ `mol^(-1)`. The longest wavelength of light capable of breaking a single Cl-Cl bond is
`(C=3xx10^(8)ms^(-1)andN=6.02xx10^(23)mol^(-1))`

Options

A. 594 nm
B. 640 nm
C. 700 nm
D. 494 nm

Explanation

To find the longest wavelength of light capable of breaking a single Cl-Cl bond in Cl₂, we can follow these steps:

### Step 1: Convert Energy from kJ/mol to J/molecule
The energy required to break one mole of Cl-Cl bonds is given as 242 kJ/mol. We first convert this energy into joules per molecule.

\[ \text{Energy in J/mol} = 242 \, \text{kJ/mol} \times 10^3 \, \text{J/kJ} = 242000 \, \text{J/mol} \]

Now, to find the energy per molecule, we divide this value by Avogadro's number (\(N_A = 6.02 \times 10^{23} \, \text{mol}^{-1}\)):

\[ E = \frac{242000 \, \text{J/mol}}{6.02 \times 10^{23} \, \text{mol}^{-1}} \approx 4.02 \times 10^{-19} \, \text{J} \]

### Step 2: Use the Energy-Wavelength Relationship
The energy of a photon is related to its wavelength (\(\lambda\)) by the equation:

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

Where:
- \(h = 6.63 \times 10^{-34} \, \text{J s}\) (Planck's constant)
- \(c = 3 \times 10^8 \, \text{m/s}\) (speed of light)

We can rearrange this equation to solve for \(\lambda\):

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

### Step 3: Substitute the Values
Now we can substitute the values of \(h\), \(c\), and \(E\) into the equation:

\[ \lambda = \frac{(6.63 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{4.02 \times 10^{-19} \, \text{J}} \]

Calculating this gives:

\[ \lambda \approx \frac{1.989 \times 10^{-25} \, \text{J m}}{4.02 \times 10^{-19} \, \text{J}} \approx 4.94 \times 10^{-7} \, \text{m} \]

### Step 4: Convert Wavelength to Nanometers
To express the wavelength in nanometers (1 nm = \(10^{-9}\) m):

\[ \lambda \approx 4.94 \times 10^{-7} \, \text{m} = 494 \, \text{nm} \]

### Conclusion
The longest wavelength of light capable of breaking a single Cl-Cl bond is approximately **494 nm**.

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