The condition under which a microwave oven heats up a food item containing water molecules most efficiently is
a. The frequency of the microwave must match the resonant frequency of the water molecule.
b. The frequency of the microwave has no relation with the natural frequency of the water.
c. Microwaves are heat waves so they always provide heating.
d. Infra-red waves produce heating in the microwave oven.

Hint: The rate at which the energy is transferred depends on the resonance, so maximum energy can be transferred at resonance. The resonance is defined as the phenomenon in which the frequency of the oscillation becomes equal or very close to the natural frequency.

Formula used:
The formula of the wavelength is given by,
$ \Rightarrow \lambda = \dfrac{c}{f}$
Where the wavelength is $\lambda $, the speed of light is $c$ and the frequency is $f$.

Complete step by step answer:
Micro-waves has the following range of frequency and wavelength-
Frequency range:-${10^9}$ to $3 \times {10^{11}}$ Hz.
The wavelength corresponding to the frequency range will be,
The formula of the wavelength is given by,
$ \Rightarrow \lambda = \dfrac{c}{f}$
Where the wavelength is $\lambda $, the speed of light is $c$ and the frequency is$f$.
The upper point of the wavelength is given by,
$ \Rightarrow \lambda = \dfrac{c}{f}$
$ \Rightarrow \lambda = \dfrac{{3 \times {{10}^8}}}{{{{10}^9}}}$
$ \Rightarrow \lambda = 3 \times {10^{8 - 9}}$
$ \Rightarrow \lambda = 3 \times {10^{ - 1}}$
$ \Rightarrow \lambda = 0 \cdot 3m$
And the lower point of the wavelength will be,
$ \Rightarrow \lambda = \dfrac{c}{f}$
$ \Rightarrow \lambda = \dfrac{{3 \times {{10}^8}}}{{3 \times {{10}^{11}}}}$
$ \Rightarrow \lambda = {10^{8 - 11}}$
$ \Rightarrow \lambda = {10^{ - 3}}m$
$ \Rightarrow \lambda = 0 \cdot 001m$

Wavelength range: 0.001m to 0.3m

Now the rate at which energy is transferred is depending upon the resonance. It means that at resonance maximum energy can be transferred. Clearly when the frequency of the microwave matches with the resonant frequency of the water molecule at that time maximum heat energy can be transferred. That’s why microwaves can heat up food.

Hence, the correct answer is option (A).

Note: Remember that microwaves are not the heating waves they just heat up whenever there is resonance, because the rate of energy transfer is maximum in resonance. The resonance is the phenomenon which can be very dangerous sometimes as whenever the army is marching through the bridge it is advised to them not to make the boot sound together because if the frequency of their boot sound matches with the frequency of the bridge then there can be huge destruction and the bridge can break too.