The energy required to break one mole of Cl-Cl bonds in Cl2 is 242 kJ mol-1 | Chemca Solution

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The energy required to break one mole of Cl-Cl bonds in Cl₂ is 242 kJ mol^-1. The longest wavelength of light capable of breaking a single Cl-Cl bond is:

Given: \( c = 3 \times 10^8 \text{ m s}^{-1} \) and \( N = 6.02 \times 10^{23} \text{ mol}^{-1} \)

(a) 494 nm

(b) 594 nm

(c) 640 nm

(d) 700 nm

Detailed Step-by-Step Solution

To find the longest wavelength of light capable of breaking a single Cl-Cl bond, we need to determine the energy required to break just one bond, and then use the Planck-Einstein relation to find the corresponding wavelength.

Step 1: Calculate energy required for one single bond

We are given the energy for one mole of bonds:

\( E_{\text{mole}} = 242 \text{ kJ mol}^{-1} = 242 \times 10^3 \text{ J mol}^{-1} \)

To find the energy for a single bond (\(E_{\text{bond}}\)), we divide by Avogadro's number (\(N_A\)):

\( E_{\text{bond}} = \frac{E_{\text{mole}}}{N_A} \)

\( E_{\text{bond}} = \frac{242 \times 10^3 \text{ J}}{6.02 \times 10^{23}} \)

\( E_{\text{bond}} \approx 4.0199 \times 10^{-19} \text{ J} \)

Step 2: Relate Energy to Wavelength

According to the Planck-Einstein relation, the energy of a photon is related to its wavelength (\(\lambda\)) by the formula:

\( E = \frac{hc}{\lambda} \)

Rearranging this formula to solve for wavelength (\(\lambda\)):

\( \lambda = \frac{hc}{E} \)

Where Planck's constant \( h = 6.626 \times 10^{-34} \text{ J s} \) and the speed of light \( c = 3 \times 10^8 \text{ m s}^{-1} \).

Step 3: Calculate the Wavelength

Substitute the values into our rearranged equation:

\( \lambda = \frac{(6.626 \times 10^{-34} \text{ J s}) \times (3 \times 10^8 \text{ m s}^{-1})}{4.0199 \times 10^{-19} \text{ J}} \)

\( \lambda = \frac{19.878 \times 10^{-26}}{4.0199 \times 10^{-19}} \text{ m} \)

\( \lambda \approx 4.944 \times 10^{-7} \text{ m} \)

To convert meters to nanometers (nm), we multiply by \(10^9\):

\( \lambda = 4.944 \times 10^{-7} \times 10^9 \text{ nm} = 494.4 \text{ nm} \)

Conclusion: The calculated wavelength is approximately 494 nm. Therefore, the correct option is (a) 494 nm.

Enhance Your Chemistry Preparation

The problem discussed above is a classic application of the photoelectric and quantum mechanical principles. It is crucial for competitive exams like JEE and NEET. To deeply understand the relationship between photons, energy, and electromagnetic radiation, we highly recommend reviewing our detailed notes on the Structure of Atom Class 11 Chemistry.

Looking for more chapter-wise solutions, NCERT explanations, and mock tests?

• Explore our complete repository for Class XI Chemistry to strengthen your fundamentals.
• Gearing up for your board exams? Dive into our advanced curriculum and study materials for Class XII Chemistry.

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