Question

Question: Which of the following has the higher energy:

(a) light having a of ${\mathbf{10}}^{\mathbf{4}}$ Hz or ${\mathbf{10}}^{\mathbf{8}}$ Hz;

(b) light having a λ of 10 nm or 1000 nm;

(c) red light or blue light?

Short answer

Answer

(a) Light having a frequency of ${10}^8$Hz.

(b) Light having a wavelength of 10 nm.

(c) Blue light.

Step-by-step solution

Energy of electromagnetic radiation

Electromagnetic radiations can be described as a stream of particles containing a certain amount of energy called photons.

Electromagnetic radiations can therefore be defined by the energy of a photon.

For a molecule to absorb radiation, the difference between energy states in a molecule should be equal to the energy of radiation.

Calculation of energy of a photon

The energy of a photon is directly proportional to its frequency.

By Planck’s Quantum theory, the energy of a photon is given by:

$\mathrm{E}=\mathrm{h\nu }$

where h is the Planck’s constant and role="math" localid="1649144673301" $\mathrm{\nu }$is the frequency of the photon.

Comparing energy of two photons

The energy of a photon is directly proportional to the frequency and inversely proportional to its wavelength.

Therefore,

• Higher frequency photons will have higher energy.
• The higher the wavelength of the photon, the lower is its energy.

(a) Light having a frequency of ${10}^8$Hz will have higher energy than light having a frequency of ${10}^4$Hz.

(b) Light having a wavelength of 10 nm will have higher energy than light having a wavelength of 1000 nm.

(c) Blue light has a higher frequency than red light. Therefore, the energy of blue light is higher than red light.