Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics.
Question:

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)].

Solution:

(a) Radio waves; it belongs to the short wavelength end of the electromagnetic spectrum.

(b) Radio waves; it belongs to the short wavelength end.

(c) Temperature, T = 2.7 °K

λis given by Planck’s law as:

$\lambda_{m}=\frac{0.29}{2.7}=0.11 \mathrm{~cm}$

This wavelength corresponds to microwaves.

(d) This is the yellow light of the visible spectrum.

(e) Transition energy is given by the relation,

E = hν

Where,

= Planck’s constant = 6.6 × 10−34 Js

ν = Frequency of radiation

Energy, = 14.4 K eV

$\therefore v=\frac{E}{h}$

$=\frac{14.4 \times 10^{3} \times 1.6 \times 10^{-19}}{6.6 \times 10^{-34}}$

$=3.4 \times 10^{18} \mathrm{~Hz}$

This corresponds to X-rays.

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