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) 21 cm wavelength belongs to ratio waves region of electromagnetic belongs to ratio waves region of electromagnetic spectrum because
` lamda = (c )/(v ) = ( 3 xx 10^8) /( 1.057 xx 10^9 )`
` =28.3 cm `
(c ) from Wien.s displacement law ,
` lamda _m ( 0.29 )/(T ) = ( 0.29 )/( 2.7 ) = 0.11 cm .`
so ` lamda = ( 1240 eV - nm )/( E ( i n eV )) `
`= ( 1240 eV -nm ) /( 14.4 xx 10 ^3 eV ) = 0.086 nm .`
This wavelength belongs to X - ray ( or soft - ` gamma - `rays region of electromagnetic spectrum .