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  • The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively.  The longest wavelength of light capable of breaking the C - C bond is <img alt="\left ( Av

The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively.  The longest wavelength of light capable of breaking the C - C bond is

\left ( Avogadro\: number \right= 6.02\times 10^{23} \: ,h= 6.62\times 10^{-34}Js)  :

Option: 1

1.49\times 10^{3}nm


Option: 2

2.48\times 10^{3}nm


Option: 3

2.48\times 10^{4}nm


Option: 4

1.49\times 10^{4}nm


Answers (1)

best_answer

The heat of the atomization of methane is 360 kJ/mol.
This corresponds to the breaking of four C−H bonds.

Hence, the heat corresponding to the breaking of one C−H bond is 

\frac{360}{4}=90\ \mathrm{kJ} \mathrm{mol}

The heat of atomization of ethane is 620 kJ/mol.

This corresponds to the breaking of one C−C bond and six C−H bonds.

The heat corresponding to the breaking of on C-C bond will be 620−6(90)=80 kJ/mol 
This corresponds to 1 mole. For one single bond, the required energy that can be obtained by dividing with Avogadro's number is given by

\mathrm{E}=\frac{80 \times 1000}{6.02 \times 10^{23}}

The energy is related to wavelength by relation

\mathrm{E}=\frac{\mathrm{hc}}{\lambda}

Substitute values in the above expression.

\frac{80 \times 1000}{6.02 \times 10^{23}}=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{\lambda}

\text { Hence, } \lambda=1.49 \times 10^{-6} \quad \mathrm{m}=1.49 \times 10^{3} \quad \mathrm{nm}

Posted by

Divya Prakash Singh

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