Question

Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A typical carbon–carbon bond requires 348 kJ/mol to break. What is the longest wavelength of radiation with enough energy to break carbon–carbon bonds?

Answer 1

Answer:

343.98 nm is the longest wavelength of radiation with enough energy to break carbon–carbon bonds.

Explanation:

A typical carbon–carbon bond requires 348 kJ/mol=348000 J/mol

Energy required to breakl sigle C-C bond:E

$E=\frac{348000 J/mol}{6.022\times 10^{23} mol^{-1}}=5.7788\times 10^{-19} J$

$E=\frac{h\times c}{\lambda}$

where,

E = energy of photon

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $3\times 10^8m/s$

$\lambda$ = wavelength of the radiation

Now put all the given values in the above formula, we get the energy of the photons.

$\lambda =\frac{(6.63\times 10^{-34}Js)\times (3\times 10^8m/s)}{5.7788\times 10^{-19} J}$

$\lambda =3.4398\\times 10^{-7}m=343.98 nm$

$1 m = 10^{9} nm$

343.98 nm is the longest wavelength of radiation with enough energy to break carbon–carbon bonds.