Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A carbon-sulfur bond requires 272 kJ/mol to break. What is the longest wavelength of radiation with enough energy to break carbon-sulfur bonds

439.7nm

Explanation:

Energy of a quantum can be calculated using below formula

E=hveqn(1)

But v=λ/ c eqn(2)

If we substitute eqn(2) into eqn(1) we have

E= hc/(λ)

Where E= energy

h= Plank's constant= 6.62607004 × 10-34 m2 kg / s

c= speed of light

c= 2.998 × 10^8 m/s

λ= wavelength= ?

But the energy was given in Kj , it must be converted to Kj/ photon for unit consistency.

Energy E= 272 kJ/mol × 1mol/6.02× 10^23

Energy= 451.83× 10^-24 Kj/ photon

E= hc/(λ)eqn(1)

If we make λ subject of the formula

λ= hc/E

Then substitute the values we have

λ= [(6.626 × 10^-34) × (2.998 × 10^8)]/451.83× 10^-24

λ=(0.00043965) × (1Kj/1000J) × (10^9nm/1m)

λ=439.7nm

Hence, the longest wavelength of radiation with enough energy to break carbon-sulfur bonds is 439.7nm

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