88 2 Quantum Mechanics – I
Natural units
=c= 1 (2.7)Mosley’s law (for characteristic X-rays)
√
ν=A(Z−b) (2.8)whereZis the atomic number,Aandbare constants.
ForKαline
λ=1 , 200
(Z−1)^2
A ̊ (2.9)
X-rays absorption
I=I 0 e−μx (2.10)Duane–Hunt law (for continuous X-rays)
λc=c
νmax=
hc
eV=
1 , 240
V
pm (2.11)whereeis the electron charge andVis the P.D through which the electrons have
been accelerated in the X-ray tube.
Doppler effect(Non-relativistic)
ν=ν 0 (1+βccosθ∗) (2.12)whereνis the observed frequency,ν 0 the frequency of light in the rest frame of
source emitted at angleθ∗,ν=βcis the source velocity. The inverse transforma-
tion is
ν 0 =ν(1−βccosθ) (2.13)
Hydrogen atom(Bohr’s model)
Angular momentum
L=n, n= 1 , 2 , 3 ..... (2.14)Energy of photon emitted from energy levelEito final levelEf.
hv=Ei−Ef (2.15)Radius of thenth orbit
rn=ε 0 h^2 n^2
πμe^2 z