Heat of atomization: CH₄ has x kJ/mol (4 C-H bonds), C₂H₆ has y kJ/mol (1 C-C + 6 C-H bonds)
Let C-H bond energy = a, C-C bond energy = b
Then: x = 4a and y = b + 6a
Solving: a = x/4, so b = y - 6x/4 = (4y - 6x)/4 kJ/mol
Converting to J/mol: b = (4y - 6x) × 250 J/mol
Using E=λhc and λ=Ehc:
λ=250(4y−6x)NAhc (in SI units)