(a)
Hint: Recall electromagnetic spectrum.
Step: Find the spectrum corresponding to a wavelength of 21 cm.
Radio waves belong to the short-wavelength end of the electromagnetic spectrum.

(b)
Hint: \(\lambda=\frac{c}{\nu}\)
Step 1: Find the wavelength of 1057 Mhz
\(\lambda=\frac{c}{\nu}=\frac{3\times10^{8}}{1057\times10^{6}}\times 100 \text{ cm}=28.3 \text{ cm}\)
Step 2: Find the spectrum corresponding to a wavelength of 28.3 cm.
Radio waves belong to the short-wavelength end of the electromagnetic spectrum.

(c)
Hint: Recall Planck's law
Step 1: Find the wavelength corresponding to the temperature of 2.7 °K
Temperature, T= 2.7 °K
$\mathrm{<br>\; According} \mathrm{to} \mathrm{Planck}\text{'}\mathrm{s} \mathrm{law}:$
${\mathrm{\lambda }}_{\mathrm{_m}}T=\frac{0.29}{}=$\(\frac{0.29}{2.7}\)=0.11 cm
Step 2: Find the spectrum corresponding to a wavelength of 0.11 cm.
This wavelength corresponds to microwaves.

(d)
Hint: Recall electromagnetic spectrum.
Step: Find the spectrum corresponding to 5890 Å - 5896 Å [double lines of sodium].
This is the yellow light of the visible spectrum.

(e)
Hint: $\mathrm{E}=\mathrm{h\nu }$
step: Find the spectrum corresponding to the energy of 14.4 keV.
Transition energy is given by the relation,

$\mathrm{E}=\mathrm{h\nu }$
$\mathrm{where} \mathrm{h} = \mathrm{Planck}\text{'}\mathrm{s} \mathrm{constant} = 6.6 \times {10}^{-34}\mathrm{Js}$
$\mathrm{\nu }=\mathrm{frequency} \mathrm{of} \mathrm{radiation}$
$\Rightarrow \mathrm{\nu }=\frac{\mathrm{E}}{\mathrm{h}}=\frac{14.4\times {10}^3\times 1.6\times {10}^{-19}}{6.6\times {10}^{-34}}$
$=3.4\times {10}^{18} \mathrm{Hz}$
This corresponds to X-rays.