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 since `Cl-Cl` bond is

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 the 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 need to convert this energy into joules per molecule because the energy of a single bond is what we are interested in.

1 kJ = 1000 J, so:
\[ 242 \text{ kJ/mol} = 242 \times 1000 \text{ J/mol} = 242000 \text{ J/mol} \]

Now, to find the energy per molecule, we divide by Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol):
\[ E_{\text{per molecule}} = \frac{242000 \text{ J/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \approx 4.02 \times 10^{-19} \text{ J/molecule} \]

### Step 2: Use the energy-wavelength relationship
The energy of a photon is related to its wavelength by the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy of the photon (in joules),
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \text{ J s}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \text{ m/s}\)),
- \(\lambda\) is the wavelength (in meters).

Rearranging the equation to solve for wavelength gives:
\[ \lambda = \frac{hc}{E} \]

### Step 3: Substitute the values into the equation
Now we can substitute the values we have into the equation:
\[ \lambda = \frac{(6.626 \times 10^{-34} \text{ J s})(3.00 \times 10^8 \text{ m/s})}{4.02 \times 10^{-19} \text{ J}} \]

Calculating this gives:
\[ \lambda \approx \frac{1.9878 \times 10^{-25} \text{ J m}}{4.02 \times 10^{-19} \text{ J}} \approx 4.94 \times 10^{-7} \text{ m} \]

### Step 4: Convert meters to nanometers
To express the wavelength in nanometers (1 nm = \(10^{-9}\) m):
\[ \lambda \approx 4.94 \times 10^{-7} \text{ m} = 494 \text{ nm} \]

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

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