The energy of a photon is represented by the expression,

$\mathrm{E}=\mathrm{hv}=\frac{h c}{\lambda}$

Where,

$\mathrm{h}$ is the planck’s constant with a value of$6.6 \times 10^{-34} J_{S}$

$\mathrm{c}$ is the speed of light with a value of $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$

If the energy is in Joule and the wavelength $\lambda$ is in metre, then by dividing $E$ by $1.6 \times 10^{-19}$ will convert the energy into $\mathrm{eV}$.

$E=\frac{h c}{\lambda \times 1.6 \times 10^{-19}} e V$

a) Because the wavelength of gamma rays runs from $10^{-10}$ to $10^{-14} \mathrm{~m}$, the photon energy can be computed as follows:

$E=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{10^{-10} \times 1.6 \times 10^{-19}}=12.4 \times 10^{3} \approx 10^{4} \mathrm{eV}$

So,

$\lambda=10^{-10} \mathrm{~m}$, energy $=10^{4} \mathrm{eV}$

$\lambda=10^{-14} \mathrm{~m}$, energy $=10^{8} \mathrm{eV}$

The range for the energy of Gamma rays is $10^{4}$ to $10^{8} \mathrm{eV}$.

b) The wavelength for $X$-rays ranges between $10^{-8} \mathrm{~m}$ to $10^{-13} \mathrm{~m}$

For $\lambda=10^{-8}$,

Energy will be $=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{10^{-8} \times 1.6 \times 10^{-19}}=124 \approx 10^{2} \mathrm{eV}$

For $\lambda=10^{-13} \mathrm{~m}$, energy $=10^{7} \mathrm{eV}$

c) For ultraviolet radiation, the wavelength ranges from $4 \times 10^{-7} \mathrm{~m}$ to $6 \times 10^{-7} \mathrm{~m}$.

For $4 \times 10^{-7} \mathrm{~m}$,

Energy will be $=\frac{6.62 \times 10^{-34} \times 3 \times 10^{8}}{4 \times 10^{-7} \times 1.6 \times 10^{-19}}=3.1 \approx 10^{10} \mathrm{eV}$

For $6 \times 10^{-7} \mathrm{~m}$, the energy is equal to $10^{3} \mathrm{eV}$.

The energy of the ultraviolet radiation has a variation between $10^{10}$ to $10^{3} \mathrm{eV}$.

d) The wavelength ranges from $4 \times 10^{-7} \mathrm{~m}$ to $7 \times 10^{-7} \mathrm{~m}$ for visible light.

The energy is the same as above for $4 \times 10^{-7}$

The energy is $100 \mathrm{eV}$ for $7 \times 10^{-7} \mathrm{~m}$,

e) The wavelength range if from $7 \times 10^{-7} \mathrm{~m}$ to $7 \times 10^{-14} \mathrm{~m}$ for infrared radiation

$100 \mathrm{eV}$ is The energy for $7 \times 10^{-7} \mathrm{~m}$.

$10^{-3} \mathrm{eV}$ is the energy for $7 \times 10^{-14} \mathrm{~m}$

f) The wavelength range is $1 \mathrm{~mm}$ to $0.3 \mathrm{~m}$ for microwaves

$10^{-3} \mathrm{eV}$ is the energy for $1 \mathrm{~mm}$.

$10^{-6} \mathrm{eV}$ is the energy for $0.3 \mathrm{~m}$.

g) For radio waves, the wavelength ranges from $1 \mathrm{~m}$ to few $\mathrm{km}$.

For $1 \mathrm{~m}$, the energy is $10^{-6} \mathrm{eV}$.

The photon energies for distinct regions of a source’s spectrum reflect the spacing of the source’s relevant energy levels.