Question

Ionization energy is the energy required to remove an electron from an atom in the gas phase. The ionization energy of magnesium is 735.0 kJ/mol. Calculate the maximum wavelength of light that will ionize magnesium.

a. 262 nm
b. 175 nm
c. 134 nm
d. 96 nm

Answer 1

To find the maximum wavelength of light that can ionize magnesium, convert the ionization energy to joules per photon and use the equation E = hc/λ to calculate the wavelength, resulting in a wavelength of approximately 163 nm.

Step-by-step explanation:

The question concerns calculating the maximum wavelength of light that can ionize magnesium. Given that the ionization energy of magnesium is 735.0 kJ/mol, we can use the relationship between energy (E), Planck's constant (h), and the speed of light (c) through the equation E = hc/λ, where λ is the wavelength.

Firstly, convert the ionization energy from kJ/mol to J/photon:

735.0 kJ/mol × (1×103 J/kJ) × (1 mol/6.022×1023 photons) = 1.22×10-18 J/photon

Next, using the equation E = hc/λ with h = 6.626×10-34 J·s and c = 3.00×108 m/s,

λ = hc/E = (6.626×10-34 J·s × 3.00×108 m/s) / 1.22×10-18 J/photon = 1.63×10-7 m = 163 nm

The maximum wavelength of light that can ionize magnesium is 163 nm, which means the closest answer would be (c) 134 nm since we round up to the nearest given option.