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

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