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) The wavelength emitted by atomic hydrogen in interstellar space i.e. 21 cm is the radio waves as radio waves are shortest in wavelength of the electromagnetic spectrum.
(b) The frequency of radiation arising from the two close energy levels in hydrogen known as Lamb shift i.e. 1057 MHz is radio waves as it belongs to the short wavelength end of the electromagnetic spectrum.
(c) Given: Temperature = 2.7 K
λm = 0.29/T cm K
putting the value of temperature in above equation
λm = 0.29/2.7 cm K
λm = 0.11 cm
The above wavelength belongs to the microwaves of the electromagnetic spectrum.
(d) 5890 Å - 5896 Å [double lines of sodium] belongs to the yellow light of the visible spectrum of electromagnetic waves.
(e) Given: Energy E = 14.4 keV
Energy is given by the relation E = hv
h = 6.6 × 10-34 Js
v = E/h
⇒ 
4 × 1018 Hz
the electromagnetic spectrum belongs to X-rays.