Question

using Balmer series calculate ionization energy of hydrogen atom in kilo joule per mole

Answer 1

We can use the Rydberg Expression to find the energy needed to move an electron from the n=1 energy level to the n=∞ energy level which means the atom is effectively ionised.

1λ=R[1n21−1n22]

Where n1< n2

In this case n2=∞ so this becomes:

1λ=R12=R

∴λ=IR

We need to correct the units of the Rydberg Constant to m−1⇒

R=1.097×107m−1

So the wavelength of the photon required to eject the electron will be given by:

λ=11.097×10−7=9.1157×10−8m

The energy of the photon is given by:

E=hf=hcλ=6.626×10−34×3×1089.1157×10−8=2.180×10−18J

This is the energy required to ionise a single atom. To find the energy required to ionise 1 mole of atoms we need to x by the Avogadro Constant:

E=2.180×10−18×6.02×1023=13.1×105J/mol

Convert to kJ by dividing by 1000 ⇒

E=1310kJ/mol