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 hatA-5896hatA` (double lines of sodium]
(e) 14.4keV energy of a particular transition in `.^(57)Fe` nucleus associated with a famour high resolution spectroscopic method (mossbauer spectroscopy).

Explanation

(a) This wavelength corresponds to radio waves (short wavelength or high freqenncy end).
(b) This frequency alos corresponds to radio wave (short wavelength or high frequency end).
(c) Given `T=2.7^@K As lambda_mT=0.29cm^@K`
`:. Lambda_m=0.29/T=0.29/2.7~=0.11 cm`
This wavelength corresponds to microwave region of the electromagnetic spectrum.
(d) This wavelength lies in the visible region (yellow) of the electromagnetic spectrum,
(e) Here, Energy `E=14.4 keV=14.4xx10^3xx1.6xx10^-19J`
As `e=hv:. v=E/h=(14.4xx10^3xx1.6xx10^-19)/(6.6xx10^-34)~=3xx10^11MHz`
This frequency lies in the X-ray region of the electromagnetic spectrum,