Calculate the wavelength of light required to break the bond between two Cl atoms in `Cl_(2)` molecules `((BE)_(Cl-Cl)= 243 kJ mol^(-1))`

Options

A. 8180 `Å`
B. `9860Å`
C. `4930Å`
D. 500nm

Answer

To calculate the wavelength of light required to break the bond between two Cl atoms in Cl2 molecules, we can follow these steps:

### Step 1: Convert Bond Energy to Joules
The bond energy (BE) given is 243 kJ/mol. We need to convert this energy into joules for one molecule.

\[ \text{Energy per mole} = 243 \, \text{kJ/mol} = 243 \times 10^3 \, \text{J/mol} \]

To find the energy for one molecule, we divide by Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{molecules/mol}\)):

\[ E = \frac{243 \times 10^3 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{molecules/mol}} = \frac{243 \times 10^3}{6.022 \times 10^{23}} \approx 4.03 \times 10^{-19} \, \text{J} \]

### Step 2: Use the Energy-Wavelength Relationship
The relationship between energy (E) and wavelength (\(\lambda\)) is given by the equation:

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

Where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\))
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\))

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

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

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

\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.00 \times 10^8 \, \text{m/s})}{4.03 \times 10^{-19} \, \text{J}} \]

Calculating this gives:

\[ \lambda \approx \frac{1.9878 \times 10^{-25}}{4.03 \times 10^{-19}} \approx 4.93 \times 10^{-7} \, \text{m} \]

### Step 4: Convert Meters to Angstroms
Since 1 Angstrom (Å) is \(10^{-10}\) meters, we convert the wavelength from meters to Angstroms:

\[ \lambda \approx 4.93 \times 10^{-7} \, \text{m} = 4930 \, \text{Å} \]

### Final Answer
The wavelength of light required to break the bond between two Cl atoms in Cl2 molecules is approximately **4930 Å**.

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