Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol–1.

Given:

Wavelength, λ = 242 nm


Finding Energy of Photon:


By Planck’s relation we have,


Energy, E = h×v


But we know v = [c] / [λ]


Where


c = Speed of Light


v= Frequency


λ = Wavelength


So, E = hc /λ


= [[6.626×10-34] × [3×108]] / [242×10-9]


= [1.9878×10-25] / [242×10-9]


= 8.214×10-19 J/atom


To convert the energy from J/atom to kJ mol–1 we carry out the following conversion process:


E = [8.214×10-19× 6.023×1023] / 1000


= [494.729× 103] / 1000


= 494.729 kJ/mol


Therefore, the energy of the photon 494.73 kJ/mol


14