2.3 Solutions 111
2.34 By Moseley’s law
1
λ=A(Z 1 −1)^2 =A(19−1)^2 (1)
1
λ/ 4=A(Z−1)^2 (2)
Dividing (2) by (1) and solving forZ, we getZ= 372.3.4 Spin andμand Quantum Numbers – Stern–Gerlah’s
Experiment
2.35 The existence of electron spin and its value was provided by the Stern–Gerlah
experiment in which a beam of atoms is sent through an inhomogeneous mag-
netic field.
Schematic representation of the Stern–Gerlah experiment. to a force moment
tending to align the magnetic moment along the field direction, but also to
a deflecting force due to the difference in field strength at the two poles of
the particle. Depending on its orientation, the particle will be driven in the
direction of increasing or decreasing field strength. If atoms with all possible
orientations in the field are present, a sharp beam should be split up into 2J+ 1
components. In Fig. 2.2 the beam is shown to be split up into two components
corresponding toJ= 1 / 2
Fig. 2.2Schematic drawing
of Stern-Gerlah’s apparatus
2.36 (i) Ifl>s, then there will be 2s+1 values ofj;j=l+s,l+s− 1 ...l−s
Ifl<s, then there will be 2l+1 values ofj;j=s+l,s+l− 1 ...s−l
(ii) The spectroscopic notation for a term is^2 S+^1 LJ,s,p,d,f...refer to
l= 0 , 1 , 2 , 3 ...respectively.
Term LSJPossible values ofJ(^2) S 1 / 2 0 1/2 1/2 1/2
(^3) D 2 2123,2,1
(^5) P 3 1232,1
(iii) Obviously the term^5 P 3 cannot exist.