2.2 Problems
97
ground state and their mean kinetic energy was 2kT, estimate the magnetic
moment.
[Adapted from the University of London, Royal Holloway and Bedford New
College, 2005]
2.41 If the electronic structure of an element is 1s
2 2s
2 2 p
6 3s
2 3 p
6 3d
10 4s
2 4 p
5 ,
why can it not be (a) a transition element (b) a rare-earth element?
[Adopted from the University of Manchester 1958]
2.42 In a Stern–Gerlach experiment the magnetic field gradient is 5.0 V s m
−2 mm
−1 ,
with pole pieces 7 cm long. A narrow beam of silver atoms from an oven at
1, 250 K passes through the magnetic field. Calculate the separation of the
beams as they emerge from the magnetic field, pointing out the assumptions
you have made (Take μ = 9.27 × 10
−24 JT
−1 ]
[Adapted from the University of Durham 1962]
2.43 (a) The magnetic moment of silver atom is only 1 Bohr magneton although it
has 47 electrons? Explain.
(b) Ignoring the nuclear effects, what is the magnetic moment of an atom in
the 3p 0 state?
(c) In a Stern–Gerlah experiment, a collimated beam of neutral atoms is split
up into 7 equally spaced lines. What is the total angular momentum of the
atom?
(d) what is the ratio of intensities of spectral lines in hydrogen spectrum for
the transitions
2
2 p 1/2 → 1
2 s 1/2 and 2
2 p 3/2 → 1
2 s 1/2 ?
2.44 Obtain an expression for the Bohr magneton.
2.2.5 Spectroscopy
2.45 (a) Given the allowed values of the quantum numbers n, l, m and m s of an
electron in a hydrogen atom (b) What are the allowed numerical values of
l and m for the n = 3 level? (c) Hence show that this level can accept 18
electrons.
[Adopted from University of London 2006]
2.46 State, with reasons, which of the following transitions are forbidden for electric dipole transitions
3 D 1 →
2 F 3
2 P 3/2 →
2 S 1/2
2 P 1/2 →
2 S 1/2
3 D 2 →
3 S 1
97
ground state and their mean kinetic energy was 2kT, estimate the magnetic
moment.
[Adapted from the University of London, Royal Holloway and Bedford New
College, 2005]
2.41 If the electronic structure of an element is 1s
2 2s
2 2 p
6 3s
2 3 p
6 3d
10 4s
2 4 p
5 ,
why can it not be (a) a transition element (b) a rare-earth element?
[Adopted from the University of Manchester 1958]
2.42 In a Stern–Gerlach experiment the magnetic field gradient is 5.0 V s m
−2 mm
−1 ,
with pole pieces 7 cm long. A narrow beam of silver atoms from an oven at
1, 250 K passes through the magnetic field. Calculate the separation of the
beams as they emerge from the magnetic field, pointing out the assumptions
you have made (Take μ = 9.27 × 10
−24 JT
−1 ]
[Adapted from the University of Durham 1962]
2.43 (a) The magnetic moment of silver atom is only 1 Bohr magneton although it
has 47 electrons? Explain.
(b) Ignoring the nuclear effects, what is the magnetic moment of an atom in
the 3p 0 state?
(c) In a Stern–Gerlah experiment, a collimated beam of neutral atoms is split
up into 7 equally spaced lines. What is the total angular momentum of the
atom?
(d) what is the ratio of intensities of spectral lines in hydrogen spectrum for
the transitions
2
2 p 1/2 → 1
2 s 1/2 and 2
2 p 3/2 → 1
2 s 1/2 ?
2.44 Obtain an expression for the Bohr magneton.
2.2.5 Spectroscopy
2.45 (a) Given the allowed values of the quantum numbers n, l, m and m s of an
electron in a hydrogen atom (b) What are the allowed numerical values of
l and m for the n = 3 level? (c) Hence show that this level can accept 18
electrons.
[Adopted from University of London 2006]
2.46 State, with reasons, which of the following transitions are forbidden for electric dipole transitions
3 D 1 →
2 F 3
2 P 3/2 →
2 S 1/2
2 P 1/2 →
2 S 1/2
3 D 2 →
3 S 1