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

The heat of atomisation of methane and ethane are x kJ mol−1 and y kJ mol−1 respectively. The longest wavelength of light capable of breaking the C–C bond can be expressed in SI unit as

Q. 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) N_Ahc / 250(y − 6x)

(B) N_Ahc (y − 6x/4)⁻¹

(D) N_Ahc / 250(4y − 6x)

Correct Answer: N_Ahc / 250(4y − 6x)

Explanation

Heat of atomisation of methane:

CH₄ → C + 4H x = 4 × (C–H)

So,

C–H bond energy = x / 4

Heat of atomisation of ethane:

C₂H₆ → 2C + 6H y = 6(C–H) + (C–C)

Substitute C–H value:

y = 6(x/4) + (C–C) C–C = y − 3x/2 = (4y − 6x)/4

Energy per bond in joule:

E = (4y − 6x) × 10³ / (4N_A)

Longest wavelength required:

λ = hc / E

On substitution:

λ = N_Ahc / 250(4y − 6x)

Hence, the correct answer is option (D).

Explanation

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