Question

The wavelength of light is $8000{\text{{\AA}}}$ . The no. of photons required to provide $20{\text{J}}$ of energy is approximately:
A.$4.56 \times {10^{18}}$
B.$8 \times {10^{19}}$
C.$7 \times {10^9}$
D.$4 \times {10^7}$

Answer 1

Hint:To answer this question, you must recall the formula for the energy of a radiation as proposed by the quantum theory of radiation. According to this theory, the energy of an electromagnetic radiation is directly proportional to the frequency of the radiation wave.
Formula used:
${\text{E}} = {\text{nh}}\nu $
Where, ${\text{E}}$ is the energy of the radiation.
${\text{h}}$ is the Planck’s constant.
${\text{n}}$ is the number of photons emitted
And $\nu $ is the frequency of the radiation.

Complete step by step answer:
The quantum theory of radiation was given by Max Planck. He proposed a hypothesis that the radiant energy such as heat or light, is not emitted continuously but discontinuously in the form of small packets of energy called quanta.
We know that, speed of light is given as
${\text{c}} = \nu \lambda $
Where, ${\text{c}}$ is the speed of light
$\lambda $ is the wavelength of light
$\nu $ is the frequency of light
We can write the wavelength of light as, $\nu = \dfrac{{\text{c}}}{\lambda }$.
Using the formula, ${\text{E}} = {\text{nh}}\nu $
Or the formula can be written as \[{\text{E}} = {\text{nh}}\dfrac{{\text{c}}}{\lambda }\]
Substituting the values, we get:
$20 = {\text{n}} \times 6.626 \times {10^{ - 34}} \times \dfrac{{3 \times {{10}^8}}}{{8000 \times {{10}^{ - 10}}}}$
Solving for n, we obtain:
${\text{n}} = 8 \times {10^{19}}$ Photons.

So the correct option is B.

Note:
Planck's quantum theory of light accounts for the photoelectric effect.
In photoelectric effect, when electromagnetic radiation, such as light, hits a material, electrons are emitted. Electrons emitted in this process are known as photoelectrons. This effect is studied in solid state, condensed matter physics, and quantum chemistry to figure out conclusions about the properties of atoms, molecules and solids. The effect is commonly used in electronic devices specialized for light detection and precisely timed electron emission.