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^22 s^22 p^63 s^23 p^63 d^104 s^24 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 5.0Vsm−^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 (Takeμ= 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
22 p 1 / 2 → 12 s 1 / 2 and 2^2 p 3 / 2 → 12 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 numbersn,l,mandmsof an
electron in a hydrogen atom (b) What are the allowed numerical values of
landmfor then =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 elec-
tric 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