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2 Quantum Mechanics – I
Natural units
= c = 1
(2.7)
Mosley’s law (for characteristic X-rays)
√
ν = A(Z − b)
(2.8)
where Z is the atomic number, A and b are constants.
For K α line
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)
λ c =
c
ν max
=
hc
eV
=
1,240
V
pm
(2.11)
where e is the electron charge and V is the P.D through which the electrons have
been accelerated in the X-ray tube.
Doppler effect (Non-relativistic)
ν = ν 0 (1 + βc cos θ
∗ )
(2.12)
where ν is the observed frequency, ν 0 the frequency of light in the rest frame of
source emitted at angle θ
∗ , ν = βc is the source velocity. The inverse transformation is
ν 0 = ν(1 − βc cos θ )
(2.13)
Hydrogen atom (Bohr’s model)
Angular momentum
L = n, n = 1, 2, 3 . . . ..
(2.14)
Energy of photon emitted from energy level E i to final level E f .
hv = E i − E f
(2.15)
Radius of the nth orbit
r n =
ε 0 h
2 n
2
πμe 2 z
(2.16)
2 Quantum Mechanics – I
Natural units
= c = 1
(2.7)
Mosley’s law (for characteristic X-rays)
√
ν = A(Z − b)
(2.8)
where Z is the atomic number, A and b are constants.
For K α line
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)
λ c =
c
ν max
=
hc
eV
=
1,240
V
pm
(2.11)
where e is the electron charge and V is the P.D through which the electrons have
been accelerated in the X-ray tube.
Doppler effect (Non-relativistic)
ν = ν 0 (1 + βc cos θ
∗ )
(2.12)
where ν is the observed frequency, ν 0 the frequency of light in the rest frame of
source emitted at angle θ
∗ , ν = βc is the source velocity. The inverse transformation is
ν 0 = ν(1 − βc cos θ )
(2.13)
Hydrogen atom (Bohr’s model)
Angular momentum
L = n, n = 1, 2, 3 . . . ..
(2.14)
Energy of photon emitted from energy level E i to final level E f .
hv = E i − E f
(2.15)
Radius of the nth orbit
r n =
ε 0 h
2 n
2
πμe 2 z
(2.16)