The heat of atomisation of methane and ethane are ' x ' kJ mol -1 and ' y ' kJ mol -1 respectively. The longest wavelength ( λ ) of light capable of breaking the C - C bond can be expressed in SI unit as :

frac hc 1000 (frac y -6 x 4 ) -1

Chemistry · Thermodynamics & Thermochemistry

JEE Main 2026 — 24 January, Evening Shift — Question 63

The heat of atomisation of methane and ethane are ' x ' $\mathrm{kJ} \mathrm{mol}^{-1}$ and ' y ' $\mathrm{kJ} \mathrm{mol}^{-1}$ respectively. The longest wavelength ( $\lambda$ ) of light capable of breaking the $\mathrm{C}-\mathrm{C}$ bond can be expressed in SI unit as :

Option A:
$\frac{\mathrm{hc}}{1000}\left(\frac{\mathrm{y}-6 \mathrm{x}}{4}\right)^{-1}$
Option B:
$\frac{\mathrm{N}_{\mathrm{A}} \mathrm{hc}}{250(4 \mathrm{y}-6 \mathrm{x})}$
Correct
Option C:
$\frac{\mathrm{N}_{\mathrm{A}} \mathrm{hc}}{250(\mathrm{y}-6 \mathrm{x})}$
Option D:
$N_{A} h c\left(y-\frac{6 x}{4}\right)^{-1}$

Answer: B

Step-by-step solution

$\mathrm{CH}_{4}(\mathrm{~g}) \rightarrow \mathrm{C}(\mathrm{g})+4 \mathrm{H}(\mathrm{g}) ; \Delta_{\mathrm{r}} \mathrm{H}=\mathrm{x} \mathrm{kJ} /$ mole $\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g}) \rightarrow 2 \mathrm{C}(\mathrm{g})+6 \mathrm{H}(\mathrm{g}) ; \Delta_{\mathrm{r}} \mathrm{H}=\mathrm{y} \mathrm{kJ} / \mathrm{mole} 1000 \mathrm{x}=4 \times \varepsilon_{\mathrm{C}-\mathrm{H}}$ $1000 \mathrm{y}=1 \times \varepsilon_{\mathrm{C}-\mathrm{C}}+6 \times \varepsilon_{\mathrm{C}-\mathrm{H}}$ $\varepsilon_{\mathrm{C}-\mathrm{C}}=\left[\mathrm{y}-\frac{3 \mathrm{x}}{2}\right] \times 1000=\frac{\mathrm{hc}}{\lambda} . \mathrm{N}_{\mathrm{A}}$ (' $\lambda$ ') wavelength of photon $=\frac{\mathrm{hc} \mathrm{N}_{\mathrm{A}}}{[4 \mathrm{y}-6 \mathrm{x}] \times 250}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 24 January, Evening Shift
Subject: Chemistry
Chapter: Thermodynamics & Thermochemistry
Topic: Thermochemistry and Enthalpy Changes