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

The Correct Option is D

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