# Chemistry Class 11 NCERT Solutions: Chapter 2 Structure of Atom Part 10

Q: 31. How many electrons in an atom may have the following quantum numbers?

(a),

(b)

(a) Total number of electrons in an atom for a value of

Total number of electrons =

The given element has a fully filled orbital as

Hence, all the electrons are paired.

(b) indicates that the electrons are present in the 3s orbital. Therefore, the number of electrons having

Q: 32. Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

Since a hydrogen atom has only one electron, according to Bohr’s postulate, the angular momentum of that electron is given by:

Where,

According to de Broglie’s equation:

Substituting the value of ‘mv’ from expression (2) in expression (1):

Since ‘ represents the circumference of the Bohr orbit (r), it is proved by equation (3) that the circumference of the Bohr orbit of the hydrogen atom is an integral multiple of de Broglie’s wavelength associated with the electron revolving around the orbit.

Q: 33. What transition in the hydrogen spectrum would have the same wavelength as the balmer transition spectrum?

For the wave number associated with the Balmer transition, n=4 to n=2 is given by:

Where,

According to the question, the desired transition for hydrogen will have the same wavelength as that of

By hit and trail method, the equality given by equation (1) is true only when

in hydrogen spectrum would have the same wavelength as Balmer transition n=4 to n=2 of spectrum.

Q: 34 Calculate the energy required for the process

The ionization energy for the H atom in the ground state is