Question

By using photons of specific wavelengths, chemists can dissociate gaseous HI to produce H atoms with certain speeds. When HI dissociates, the H atoms move away rapidly, whereas the heavier I atoms move more slowly.

Given that the bond energy of H-I is 300.4 kJ/mol, what is the longest wavelength (in nm) that can dissociate a molecule of HI?

Answer 1

wavelength = 398.5 nm

Explanation

Bond energy = 300.4 kJ/mol = 300.4 x 10³ J/mol

Formula used : Bond energy = [(Planck's constant) * (speed of light) * (Avogadro's number)] / (wavelength)

where Planck's constant = 6.626 x 10^-34 J.s

speed of light = 3 x 10⁸ m/s

Avogadro's number = 6.022 x 10²³ molecules/mol

wavelength = [(Planck's constant) * (speed of light) * (Avogadro's number)] / (bond energy)

Substituting the values

wavelength = [(6.626 x 10^-34 J.s) * (3 x 10⁸ m/s) * (6.022 x 10²³ molecules/mol)] / (300.4 x 10³ J/mol)

wavelength = 3.985 x 10^-7 m

wavelength = 3.985 x 10^-7 m * (10⁹ nm / 1 m)

wavelength = 398.5 nm