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).
$(d)$ $5890 \; \mathring{A} - 5896 \; \mathring{A}$ (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, Mossbauer spectroscopy).
$(a)$ $21 \; cm$ (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).
$(d)$ $5890 \; \mathring{A} - 5896 \; \mathring{A}$ (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, Mossbauer spectroscopy).
$(a)$ 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, $T = 2.7 \; K$. According to Wien's displacement law, the wavelength $\lambda_{m}$ corresponding to maximum intensity is given by $\lambda_{m} = \frac{b}{T} \approx \frac{0.29 \; cm \cdot K}{2.7 \; K} \approx 0.11 \; cm$. This wavelength corresponds to microwaves.
$(d)$ This is the yellow light of the visible spectrum.
$(e)$ Transition energy is given by $E = h\nu$. For $E = 14.4 \; keV = 14.4 \times 10^3 \times 1.6 \times 10^{-19} \; J$, the frequency $\nu = \frac{E}{h} \approx 3.5 \times 10^{18} \; Hz$. This corresponds to $X$-rays.
$(b)$ Radio waves; it belongs to the short wavelength end.
$(c)$ Temperature, $T = 2.7 \; K$. According to Wien's displacement law, the wavelength $\lambda_{m}$ corresponding to maximum intensity is given by $\lambda_{m} = \frac{b}{T} \approx \frac{0.29 \; cm \cdot K}{2.7 \; K} \approx 0.11 \; cm$. This wavelength corresponds to microwaves.
$(d)$ This is the yellow light of the visible spectrum.
$(e)$ Transition energy is given by $E = h\nu$. For $E = 14.4 \; keV = 14.4 \times 10^3 \times 1.6 \times 10^{-19} \; J$, the frequency $\nu = \frac{E}{h} \approx 3.5 \times 10^{18} \; Hz$. This corresponds to $X$-rays.
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