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) Equation , Equation

(b) Equation

Answer:

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

Equation

Total number of electrons = Equation

Equation

The given element has a fully filled orbital as

Equation

Hence, all the electrons are paired.

Equation

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

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.

Answer:

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

Equation

Where,

Equation

According to de Broglie’s equation:

Equation

Equation

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

Equation

Equation

Since ‘ Equation 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 Equation spectrum?

Answer:

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

Equation

Where,

Equation

Equation

Equation

Equation

Equation

Equation

Equation

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

Equation

Equation

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

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

Q: 34 Calculate the energy required for the process

Equation

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

Answer:

Energy associated with hydrogen- like species is given by,

Equation

For ground state of hydrogen atom,

Equation

Equation

Equation

For the given process,

Equation

An electron is removed from Equation

Equation

Equation

Equation

Equation

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