The bond enthalpy of the C-N bond in the amide group of proteins can be treated as an average of C-N (276 kJ/mol) and C═N (615 kJ/mol) bonds. Calculate the maximum wavelength of light needed to break the amide bond.

268 nm

Explanation:

First' let's calculate the average bond energy:

(276 + 615) / 2 = 445.5 kJ/mol

By Avogadro's number 1 mol = 6.02x10²³ molecule, then the energy necessary to break the amide bond in 1 molecule is:

E = 445.5/6.02x10²³ = 7.4x10⁻²² kJ = 7.4x10⁻¹⁹ J

So, the wavelength of light (λ) can be calculated by:

E = h*c/λ

Where h is the Planck's constant (6.626x10⁻³⁴ J. s), and c is the light speed (3.0x10⁸ m/s).

7.4x10⁻¹⁹ = 6.626x10⁻³⁴ * 3.0x10⁸/λ

λ = 2.68x10⁻⁷ m

λ = 268 nm