To find the wavelength at which the dissociating effect of light can be expected for molecular chlorine, we can follow these steps:
### Step 1: Understand the Relationship Between Energy and Wavelength
The energy required for the dissociation of molecular chlorine is given as ΔH = 243.6 kJ/mol. We need to convert this energy into joules for our calculations.
**Hint:** Remember that 1 kJ = 1000 J.
### Step 2: Convert ΔH to Joules
Convert the dissociation energy from kJ/mol to J/mol:
\[
\Delta H = 243.6 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 243600 \, \text{J/mol}
\]
### Step 3: Use the Relationship Between Energy and Frequency
The energy of a photon can be expressed using the equation:
\[
E = h \cdot \nu
\]
where \(E\) is energy, \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)), and \(\nu\) is the frequency.
### Step 4: Relate Frequency to Wavelength
The frequency can also be related to wavelength (\(\lambda\)) using the speed of light (\(c\)):
\[
\nu = \frac{c}{\lambda}
\]
Substituting this into the energy equation gives:
\[
E = h \cdot \frac{c}{\lambda}
\]
### Step 5: Rearranging to Find Wavelength
Rearranging the equation to solve for wavelength:
\[
\lambda = \frac{h \cdot c}{E}
\]
### Step 6: Substitute Known Values
Now, substitute the known values into the equation:
- \(h = 6.626 \times 10^{-34} \, \text{J s}\)
- \(c = 3.00 \times 10^8 \, \text{m/s}\)
- \(E = 243600 \, \text{J/mol}\)
However, since \(E\) is given per mole, we need to divide it by Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\)) to find the energy per photon:
\[
E_{\text{photon}} = \frac{243600 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \approx 4.04 \times 10^{-19} \, \text{J}
\]
### Step 7: Calculate Wavelength
Now, substitute \(E_{\text{photon}}\) into the wavelength equation:
\[
\lambda = \frac{(6.626 \times 10^{-34} \, \text{J s}) \cdot (3.00 \times 10^8 \, \text{m/s})}{4.04 \times 10^{-19} \, \text{J}} \approx 4.91 \times 10^{-7} \, \text{m}
\]
### Step 8: Convert Wavelength to Nanometers
Convert the wavelength from meters to nanometers:
\[
\lambda \approx 4.91 \times 10^{-7} \, \text{m} = 491 \, \text{nm}
\]
### Final Answer
The wavelength at which the dissociating effect of light can be expected is approximately **491 nm**.
---
