Read the pasage given below as well as the adjoining energy level diagram and then answer the questions given after the passage .
As per Bohr's theory og hydrogen atom the energy of an atom in a state corresponding to principal quantum number n is given as :
`E_(n) = - (13.6)/(n^(2)) eV`
The energy of an atom is the least when its electron is revolving in an orbit closets to the nucleus i.e., the one for which n =1. This state is called the ground state. When a hydrogen atom receives energy by processes such as electron collision , the atom may acquire sufficient energy to raise the electron to higher energy states and the atom is then said to be in an excited state . From these excited states the electron can then fall back to a state of lower energy , emitting a photon in the process.
The energy level diagram for the stationary states of a hydrogen atom , compouted from Bohr's relation for energy , is given in Fig.12.02. The principal quantum number n labels the stationary states in the ascending order of energy . Obviously , the highest energy corresponds to `n = oo` and has an energy of 0 eV. This is the energy of the atom when the electron is completely removed `(r= oo)` from the nucleus and is at rest.

Now answer the follwoing questions:
Find a relation between wavelengths of first line and series limit of hydrogen spectrum in vissible light.

Explanation

As `(h_(c))/(lambda_(1)) = E_(3) - E_(1) = 1.89 eV and (h_(c))/(lambda_("limit")) = E_(oo) - E_(2) = 0 - (-3.40) = 3.40 eV`
`rArr " "(lambda_("limit"))/(lambda_(1)) = (1.89)/(3.40) or lambda_("limit") = (1.89)/(3.40) lambda_(1) = 0.556 lambda_(1)`