Arrange the following electromagnetic radiations per quantum in the order of increasing energy:
A: Blue light
B: Yellow light
C: X-ray
D: Radiowave

For electromagnetic radiation, the energy carried by one quantum (one photon) is given by the fundamental relation

$$E = h\nu \,,$$

where $$E$$ is the energy of the photon, $$h$$ is Planck’s constant, and $$\nu$$ (Greek letter nu) is the frequency of the radiation.

Another equally useful form of the same relation comes from the wave equation $$c = \lambda\nu$$, where $$c$$ is the speed of light and $$\lambda$$ is the wavelength. Substituting $$\nu = \dfrac{c}{\lambda}$$ into the energy equation, we obtain

$$E = h\nu = h\left(\dfrac{c}{\lambda}\right) = \dfrac{hc}{\lambda}\,.$$

This tells us clearly that

$$E \propto \nu \quad\text{and}\quad E \propto \dfrac{1}{\lambda}.$$

In simple words, higher frequency (or equivalently, shorter wavelength) means greater photon energy. Conversely, longer wavelength (or lower frequency) means smaller photon energy.

Now we list the given radiations together with their approximate wavelength or frequency ranges, just to anchor the idea:

Blue light: $$\lambda \approx 450\ \text{nm}$$ (shorter wavelength within visible)
Yellow light: $$\lambda \approx 590\ \text{nm}$$ (longer wavelength than blue)
X-ray: $$\lambda \approx 0.01\text{ nm to }10\ \text{nm}$$ (extremely short wavelength)
Radiowave: $$\lambda \approx 1\ \text{m to }10^{6}\ \text{m}$$ (very long wavelength)

Comparing wavelengths:

Radiowave has the largest $$\lambda$$ ⇒ lowest $$\nu$$ ⇒ lowest $$E$$.
Yellow light has a shorter $$\lambda$$ than radiowave but longer than blue light ⇒ its $$E$$ is higher than radiowave but lower than blue light.
Blue light has still shorter $$\lambda$$ ⇒ higher $$E$$ than yellow light.
X-ray possesses the smallest $$\lambda$$ ⇒ highest $$\nu$$ ⇒ highest $$E$$ of all in the list.

Putting them together in the order of increasing photon energy (lowest first, highest last):

Radiowave $$\longrightarrow$$ Yellow light $$\longrightarrow$$ Blue light $$\longrightarrow$$ X-ray

Symbolically, that is

$$D \; < \; B \; < \; A \; < \; C$$

This corresponds precisely to the sequence D, B, A, C.

Checking the options, we see that Option C lists the radiations in the order D, B, A, C.

Hence, the correct answer is Option C.