1000 Solved Problems in Modern Physics

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

(2.16)