Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs. (a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space). (b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift). (c) 2.7 K [temperature associated with the isotropic radiation filling all space-thought to be a relic of the ‘big-bang’ origin of the universe]. (d) 5890 Å - 5896 Å [double lines of sodium] (e) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous high resolution spectroscopic method (Mössbauer spectroscopy)].
a)
Given: The wavelength emitted by atomic hydrogen in interstellar space is 21 cm .
The wavelength 21 cm shows the radio waves because the radio waves belong to the short wavelength end of the electromagnetic spectrum.
b)
Given: The frequency of radiation arising from two close energy levels in hydrogen is 1057 MHz .
The frequency of the radiation 1057 MHz shows the radio waves because the radio waves belong to the short wavelength end of the electromagnetic spectrum.
c)
Given: Temperature-associated with the isotropic radiation filling all space through to a relic of the ‘big-bang’ origin of the universe is 2.7 ° K
The Plank’s law is given as,
λ m = 0.29 T cm
By substituting the given values in the above expression, we get
λ m = 0.29 2.7 = 0.11 cm
This wavelength corresponds to the microwaves in the electromagnetic spectrum.
d)
The range of the wavelength between 5890 A o to 5896 A o shows the yellow light of the visible spectrum.
e)
Given: The energy of a particular transition in F 57 e nucleus associated with a spectroscopic method is 14.4 MeV .
The transition energy is given as,
E = h ν v = E h
Where, h is the Plank’s constant, E is the energy and ν is the frequency of the radiation.
By substituting the given values in the above expression, we get
v = 14.4 × 10 3 × 1.6 × 10 − 19 6.6 × 10 − 34 = 3.4 × 10 18 Hz
This frequency 3.4 × 10 18 Hz corresponds to X-rays.
a)
Given: The wavelength emitted by atomic hydrogen in interstellar space is
The wavelength
b)
Given: The frequency of radiation arising from two close energy levels in hydrogen is
The frequency of the radiation
c)
Given: Temperature-associated with the isotropic radiation filling all space through to a relic of the ‘big-bang’ origin of the universe is
The Plank’s law is given as,
By substituting the given values in the above expression, we get
This wavelength corresponds to the microwaves in the electromagnetic spectrum.
d)
The range of the wavelength between
e)
Given: The energy of a particular transition in
The transition energy is given as,
Where,
By substituting the given values in the above expression, we get
This frequency
