When an electron in hydrogen atom jumps from the third excited state to the ground state how would the broccoli wavelength associated with the electron change?

Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number ni ) to the lower state, (nf ).

When electron in hydrogen atom jumps from energy state ni =4 to nf =3, 2, 1, identify the spectral series to which the emission lines belong.

According to Bohr’s postulates, in a hydrogen atom, a single electron revolves around a nucleus of charge +e. For an electron moving with a uniform speed in a circular orbit on a given radius, the centripetal force is provided by the Coulomb force of attraction between the electron and the nucleus.

Therefore, 

                                       ... (1) 

So, Kinetic Energy, K.E = 

Potential energy is given by, P.E = 

Therefore, total energy is given by, E = K.E + P.E = 

E =  , is the total energy. 

For nth orbit, E can be written as En,

                           ... (2) 

Now, using Bohr's postulate for quantization of angular momentum, we have

 

Putting this value of v in equation (1), we get

 

Now, putting value of rn in equation (2), we get

 

R is the rydberg constant. 

For hydrogen atom Z =1,

If ni and nf are the quantum numbers of initial and final states and Ei & Ef are energies of electron in H-atom in initial and final state, we have 

 

That is, when electron jumps from ni = 4 to nf = 3.21 .

Radiation belongs to Paschen, Balmer and Lyman series.

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now