Question

Use Coulomb's law to calculate the ionization energy in kJ/mol of an atom composed of a proton and an electron separated by 114.00 pm . Express your answer ro\\to three significant figures with the appropriate units.

part 2: What wavelength of light has sufficient energy to ionize the atom?

Answer 1

1)
r = 114 pm = 114*10^-12 m
for 1 atom,
E = K*q1*q2/r
= 9*10^9 * (1.602*10^-19)* (1.602*10^-19) / (114*10^-12 )
= 2.03*10^-18 J

For 1 mol of atom,
E = 2.03*10^-18 J * 6.022*10^23
= 1.22*10^6 J/mol
= 1.22*10^3 KJ/mol
Answer: 1.22*10^3 KJ/mol

2)

Given:
Energy of 1 mol = 1.22*10^3 KJ/mol
= 1.22*10^6 J/mol
Find energy of 1 photon first
Energy of 1 photon = energy of 1 mol/Avogadro's number
= 1.22*10^6/(6.022*10^23)
= 2.026*10^-18 J
This is energy of 1 photon

use:
E = h*c/lambda
2.026*10^-18J =(6.626*10^-34 J.s)*(3.0*10^8 m/s)/lambda
lambda = 9.81*10^-8 m
Answer: 9.81*10^-8 m