Question

which of the following electronic transition in a hydrogen atom would have the longest wavelenght
?
n=4 to n = 1
n=2 to n=1
n=4 to n =3
n=4 to n=2

Answer 1

Energy of an electron of Hydrogen atom in nth shell is : E = -13.6/n^2 (Energy is in eV), where -13.6 eV is the Ionisation energy of Hydrogen atom.

Since, electron jumps from n=4 to n=2,(higher energy level to lower energy level) energy will be released in the form of light (photons) whose wavelength we need to find out.

E4= -13.6/16 (energy(eV) of electron at n=4)

E2= -13.6/4 (energy(eV) of electron at n=2)

Therefore, ∆E=E4-E2= (13.6*3)/16 (in eV)

Now, from the relation, wavelength(in nm)= 1240/∆E , light of wavelength= 486.27 nm will be emitted.(visible blue light)

Since, range of wavelength of blue light (450–495) nm.

Answer 2

from 2 to 1 it has longest wavelenght