Question

Two sources of light emit with a power of 200 W.The ratio of number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be :

• A. 1 : 5
• B. 1 : 3
• C. 5 : 3
• D. 3 : 5

Answer 1

Answer: (D)

3 : 5

Answer 2

Let $n_1$ and $n_2$ be the number of photons emitted by the sources with wavelengths $\lambda_1 = 300 \, \text{nm}$ and $\lambda_2 = 500 \, \text{nm}$, respectively.

Step 1. Calculate the energy of photons for each wavelength: The power emitted by each source is given as 200 W, so:

$n_1 \times \frac{hc}{\lambda_1} = 200$

$n_2 \times \frac{hc}{\lambda_2} = 200$

Step 2. Formulate the ratio:

$\frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1}$

Substituting values:

$\frac{n_1}{n_2} = \frac{300}{500}$

Simplifying, we get:

$\frac{n_1}{n_2} = \frac{3}{5}$

Therefore, the ratio of the number of photons emitted by each source is 3 : 5.

The Correct Answer is: 3:5