Question

If mean wavelength of light radiated by 100 W lamp is \[5000\mathop A\limits^0 \], then number of photons radiated per second are
A. \[3 \times {10^{23}}\]
B. \[2.5 \times {10^{22}}\]
C. \[2.5 \times {10^{20}}\]
D. \[5 \times {10^{17}}\]

Answer 1

Hint: In this question we need to calculate the number of photons radiated per second. In order to find it, we first need to calculate the energy emitted by the photons that is converted into light by using the formula. Then, we can calculate the energy of n photons. Based on the relation between energy, power and time we can find the result.

Formula usedFormula for the power is given as,
\[P = \dfrac{\text{Work(W)}}{\text{Time(t)}} = \dfrac{\text{Energy(E)}}{\text{Time(t)}}\]
The energy emitted by the photons is given as,
\[E = \dfrac{{hc}}{\lambda }\]
Where h is Planck constant, c is the speed of light and \[\lambda \] is the wavelength.

Complete step by step solution:
Mean wavelength of light, \[\lambda = 5000\mathop A\limits^0 \]
Power, \[P = 100W\]
As we know,
\[\text{Power, P} = \dfrac{\text{Work(W)}}{\text{Time(t)}} = \dfrac{\text{Energy(E)}}{\text{Time(t)}}\]
If the energy of 1 photon is E.
Then the energy of $n$ photon is \[nE\].
\[P = \dfrac{{nE}}{t}\]

Using the formula for E,
\[P = \left( {\dfrac{n}{t}} \right)\dfrac{{hc}}{\lambda }\]
\[\dfrac{n}{t} = \dfrac{{6.62 \times {{10}^{34}}}}{{5000 \times {{10}^{ - 10}}}}\]
By solving this, we get
\[\dfrac{n}{t} = 2.5 \times {10^{20}}\]
Therefore, the number of photons radiated per second is \[2.5 \times {10^{20}}\].

Hence option C is the correct answer.

Note: The energy of a single photon emitted by the lamp can be determined by the energy formula. We are able to calculate the number of photons by simply dividing the total energy by the energy of a single photon due to the fact that electromagnetic radiation is always quantized in nature. This implies that the lamp emits light in packets of fixed energy known as photons. In physics the power is defined as the amount of energy transferred or converted from one form to the another in per unit time.