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

Longest wavelength :3.44 x 10⁻⁷ m

Step-by-step explanation:

The maximum wavelength of the radiation with enough energy to break carbon to carbon bonds will be given by:

E= hc/λ where h is Plancks constant for one photon,

c speed of light

E enrgy required per mol

One has to be careful in this problem to either multiply Planck`s constant by Avogadro's number to obtain the energy of a mol of photons or convert the given required energy per mol to energy per atom.

Substituting in our equation and doing the calculations:

λ = hc/E

λ = 6.626 x 10⁻³⁴ Js /mol x 3 x 10^8 m/s x 6.022 x 10²³8 mol / ( 3.48 x 10⁵ J = 3.44 x 10⁻⁷ m = 3440 nm which corresponds to the Infrared part of the spectrum.

Answer 2

The longest wavelength of radiation with enough energy to break a carbon–carbon bond is 343.75 nm.

Step-by-step explanation:

E = hc/λ

E: energy = 348 000 J / 6.022 x 10²³ = 5.7788 x 10⁻¹⁹ J

h: Planck's constant = 6.62607004 × 10⁻³⁴ J.s

c: speed of light = 299 792 458 m / s

λ: wavelength

λ = hc/E

λ = (6.62607004 × 10⁻³⁴ J.s x 299 792 458 m / s) / 5.7788 x 10⁻¹⁹J

λ = 3.4375 x 10⁻⁷ m

λ = 343.75 nm