Question

Ionization is removal of an electron from the ground state [lowest possible value of n] completely from the atom. Calculate the energy required to ionize a hydrogen like atom (in kJ/mol).

Answer 1

For finding the ionization energy of a hydrogen like atom we have to understand first what ionization energy means-

Ionization energy- The energy required to remove an electron from the field of the atom to infinity is called Ionization energy. That is removing it from n=1 state to n= ∞ state.

Now we will use Rydberg Expression to calculate the wavelength emmited when ionization happens by

1/λ=R*z²[(1/n1)²−(1/n2)²]

where

λ is the wavelength of the emission line

n1 is the principle quantum number of the lower energy level

n2 is the principle quantum number of the higher energy level

R is the Rydberg Constant 1.097×10⁷ m⁻¹

z is the atomic number

so putting n1=1 and n2 = ∞ and z=1 we have

1/λ= R

λ=1/R=1/1.097×10^{7 =} 9.115*10^-8 m.

now E = h*c/λ (plank's equation)

E=(6.626×10⁻³⁴×3×10⁸)/9.115*10^-8

E=13.6 eV.

converting it to joules multiply by the electronic charge

E = 13.6*1.6×10⁻¹⁹ J/mol

E =2.176*10^-21 KJ/mol.