JEE Main 2026 — Jan 24, Shift 2 — Chemistry solution

JEE Main2026Jan 24, Shift 2Chemistry

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 :

A
$\frac{h c}{1000} (\frac{y - 6 x}{4})^{- 1}$
B
$\frac{N _{A} h c}{250 ( 4 y - 6 x )}$
C
$\frac{N _{A} h c}{250 ( y - 6 x )}$
D
$N_{A} h c (y - \frac{6 x}{4})^{- 1}$

Solution

Atomisation:

$CH_{4} \to C + 4 H; Δ_{r} H = x$ kJ/mol $\Rightarrow 1000 x = 4 ε_{C-H}$

$C_{2} H_{6} \to 2 C + 6 H; Δ_{r} H = y$ kJ/mol $\Rightarrow 1000 y = ε_{C-C} + 6 ε_{C-H}$

From the first, $ε_{C-H} = 250 x$ (per mol). Substituting:

$1000 y = ε_{C-C} + 6 (250 x) \Rightarrow ε_{C-C} = (1000 y - 1500 x)$ J/mol $= 250 (4 y - 6 x)$ J/mol.

Energy per single C-C bond $= \frac{250 ( 4 y - 6 x )}{N _{A}}$ J. Setting this equal to the photon energy $\frac{h c}{λ}$ gives the longest (lowest-energy) wavelength that can still break the bond:

$λ = \frac{N _{A} h c}{250 ( 4 y - 6 x )}$ .

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