Question

1.With the aid of a labeled diagram, describe the Bohr model of the hydrogen atom.

2. Derive the following relationship for a hydrogen atom according to the Bohr model: rn = a n 2 where rn are the permitted radii of the electron orbit, n = 1, 2, 3…, and ‘a’ is a constant. Determine ‘a’ in terms of variables that you define. Hint: equate Coulomb’s law with the centripetal force acting on an electron, and then take angular momentum to be quantized according to Bohr.

3. Give a relationship for the quantum uncertainty principle, clearly defining variables. Reason why atoms don’t collapse due to this principle.

4. A hydrogen atom makes a transition from the 5th to the 2nd quantum state. What is the wavelength of light emitted? Take the allowed energies, E of a hydrogen atom to be given by: En = -(13.60 eV)/n2 where n = 1, 2, 3…

Answer 1

3. Ans The electron can revolve round the nucleus only in those circular orbits in which the angular momentum of an electron is integral multiple of h/2,where h is Planck's constant.(h=6.62 x 10^-34).

While revolving in such an orbit,the electron can not radiate energy.Such orbits are called stationary orbits.Each stationary orbit is associated with a definite amount of energy. An electron revolves in a stationary orbit without radiating energy which saves electrons from falling into the nucleus.

4.Ans.