122
2 Quantum Mechanics – I
μ = m 1 /2 = 0.5 m p
N 0 /N 1 = (1/3) exp
2 /μr
2 kT
= (1/3) exp
2 c
2 /μc
2 r
2 kT
=
1
3
exp
197.3 × 10
−15
2
0.5 × 938 ×
1.06 × 10 −10
2 ×
1.38 × 10 −23 /1.6 × 10 −13
× 300
= 0.445
2.62 ω =
k
μ
μ =
m N m 0
m N + m 0
= 7.466 amu
ω =
1550
7.466 × 1.67 × 10 −27
1/2
= 3.526 × 10
14 s
−1
E = ω =
1.055 × 10
−34
× 3.526 × 10
14
1.6 × 10 −19
= 0.2325
λ =
1,241
0.2325
nm = 5,337 nm = 5.34 μm
This wavelength corresponds to Infrared region.
2.63 (i) λ =
c
ν
=
3 × 10
8
1.153 × 10 11 = 2.6 × 10
−3 m = 2.6 mm
It lies in the microwave part of electromagnetic spectrum.
(ii) E(eV ) =
1241
λ(nm)
=
1241
2.6 × 10 6 (nm)
= 0.000477 eV
(iii) μ =
m c m 0
m c + m 0
=
12 × 16
12 + 16
= 6.857 u
(iv) E 1 =
1(1 + 1)
2
2μr 2
=
2
μr 2
E 0 = 0
ΔE = E 1 − E 0 =
2
μr 2
r =
2 c
2
μc 2 ΔE
1/2
=
197.3
2 (MeV − fm)
2
6.857 × 931.5 × 477 × 10 −12
1/2
= 0.113 × 10
−9 m
= 1.13 ˚
A
2.64 E J =
J (J + 1)
2
2I o
I o = μr
2
=
M p
2
r
2