Question

A beam of red light and a beam of blue light have equal intensities. Which of the following statements is true?

• A. The blue beam has more number of photons than the red beam.
• B. The red beam has more number of photons than the blue beam.
• C. Wavelength of red light is lesser than wavelength of blue light.
• D. The blue light beam has lesser energy per photon than that in the red light beam.

Hint:

For equal intensity, the beam with lower energy per photon must have more photons. Red light has less energy per photon than blue light.

Answer 1

The Correct Option is B

Energy of a photon is given by: \[ E = \frac{hc}{\lambda} \] Where \( h \) is Planck’s constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
- Blue light has shorter wavelength than red light, so energy per photon of blue light is greater than that of red light.
- Intensity is the total energy per unit area per unit time. If both beams have the same intensity, then:
\[ \text{Number of photons} = \frac{\text{Total energy}}{\text{Energy per photon}} \] - Since red photons have less energy, more of them are required to deliver the same intensity.
Therefore, the red beam has a greater number of photons than the blue beam. Final answer: The red beam has more number of photons than the blue beam.