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Electromagnetic Waves — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Waves5 Marks
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.
  1. $21 \ cm \ ($wavelength emitted by atomic hydrogen in interstellar space$)$.
  2. $1057 MHz \ ($frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift$).$
  3. $2.7 K \ [$temperature associated with the isotropic radiation filling all space $-$ thought to be a relic of the ‘big $-$ bang’ origin of the universe$]$.
  4. $5890 \mathring A - 5896 \mathring A \ [$double lines of sodiu$]$
  5. $14.4 keV \ [$energy of a particular transition in ${57}Fe$ nucleus associated with a famous high resolution spectroscopic method $($Mössbauer spectroscopy$)].$
✓

Answer

  1. Radio waves; it belongs to the short wavelength end of the electromagnetic spectrum.
  2. Radio waves; it belongs to the short wavelength end.
  3. Temperature $, T = 2.7 ^\circ K$
$\lambda_\text{m}$ is given by Planck's law as:
$\lambda_\text{m}=\frac{0.29}{2.7}=0.11 \ \text{ cm}$
This wavelength corresponds to microwaves.
  1. This is the yellow light of the visible spectrum.
  2. Transition energy is given by the relation,
$E = hv$
Where,
$h =$ Planck's constant $= 6.6 \times 10^{-34} Js$
$v =$ Frequency of radiation
Energy $,E = 14.4 K eV$
$\therefore \ \text{v}=\frac{\text{E}}{\text{h}}$
$=\frac{14.4\times10^3\times1.6\times10^{-19}}{6.6\times10{-34}}$
$= 3.4 \times 10^{18} Hz$
This corresponds to $X-$ rays.

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