Question

In a future hydrogen-fuel economy, the cheapest source of H2 will certainly be water. It takes 467 kJ to produce 1 mol of H atoms from water. What is the frequency, wavelength, and minimum energy of a photon that can free an H atom from water? Enter your answers in scientific notation. What is the minimum energy?

Answer 1

Find Wavelength and frequency of photon

E = h*v (E is the energy)

1 KJ = 1000 J and h (Planck's constant) = 6.626x10^-34 Js and
E = 7.75x10^-19 J

v = (E / h) = (7.75x10^-19 J)/(6.626x10^-34J.s)

v = 1.17x10¹⁵ s^-1

v = (E / h) -->> { (467kJ)(10³J/1KJ) (1mol/6.022x10²³) / (6.626x10^-34J.s) }

λ = h*c / E----->> { (6.626x10^-34J) * (3.00x10⁸) / (7.75x10^-19) }
λ = 2.56x10^-7

but it should follow in the units better.

256 nm may be a little high for the wavelength.

Recent research seems to support 243 nm or 117.59 Kcal/mol.