Bond dissociation on energy of `Cl_(2)` is 240 kJ/mol. The longest wavelength of photon that can break this bond would be `[N_(A)=6xx10^(23), h=6.6xx10^(-34)J/s]`

Options

A. `4.95xx10^(-7)m`
B. `9.9xx10^(-7)m`
C. `4.95xx10^(-6)m`
D. `9.9xx10^(-6)m`

Answer

To solve the problem of finding the longest wavelength of a photon that can break the bond of Cl₂, we will follow these steps:

### Step 1: Convert Bond Dissociation Energy to Joules
The bond dissociation energy of Cl₂ is given as 240 kJ/mol. We need to convert this energy into joules.

\[ \text{Energy in Joules} = 240 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 240000 \, \text{J/mol} \]

### Step 2: Calculate Energy Required for One Molecule
To find the energy required to break a single Cl-Cl bond, we divide the total energy by Avogadro's number (N_A = \(6 \times 10^{23}\) mol⁻¹).

\[ E_{\text{single bond}} = \frac{240000 \, \text{J/mol}}{6 \times 10^{23} \, \text{mol}^{-1}} = 4 \times 10^{-19} \, \text{J} \]

### Step 3: Use the Energy-Wavelength Relationship
The energy of a photon can be expressed in terms of its wavelength using the formula:

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

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

### Step 4: Rearranging the Formula for Wavelength
To find the wavelength, we rearrange the formula:

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

### Step 5: Substitute the Values
Now we can substitute the values of \(h\), \(c\), and \(E\) into the equation:

\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^{8} \, \text{m/s})}{4 \times 10^{-19} \, \text{J}} \]

### Step 6: Calculate the Wavelength
Calculating the above expression:

\[ \lambda = \frac{1.9878 \times 10^{-25} \, \text{J m}}{4 \times 10^{-19} \, \text{J}} = 4.9695 \times 10^{-7} \, \text{m} = 496.95 \, \text{nm} \]

### Final Answer
The longest wavelength of a photon that can break the Cl₂ bond is approximately **497 nm**.

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