Question

Question 8.14: 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 57 Fe nucleus associated with a famous high resolution spectroscopic method (Mössbauer spectroscopy)].

Class 12 - Physics - Electromagnetic Waves Electromagnetic Waves Page-287

Answer 1

(a) we know,
$\bf{\nu=\frac{c}{\lambda}}$
so, frequency = 3 × 10^8/(21 × 10^-2)
= 0.1438 × 10^10 Hz
= 1438 × 10^6 Hz
= 1438 MHz

(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) Using Wein's law the wavelength of the radiation mostly emitted at given temperature of heavenly bodies can he calculated as
$\lambda_m\times T=b=0.29cmK\\or,\lambda_m=\frac{b}{T}=0.29/2.7=0.11cm$
this wavelength correspond to microwave region of electromagnetic waves.

(d) 5890 A° - 5896 A° [double lines of sodium] belongs to the yellow light of the visible spectrum of electromagnetic waves.

(e) The frequency of radiation can be calculated as E = hv,
v = E/h = (14.4 × 10^3 × 1.6 × 10^-19)/(6.626 × 10^-34)
v = 3.49 × 10^18 Hz
this frequency correspond to X - ray region of electromagnetic waves.