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

Photon energy is calculated using the formula: \[ E = \frac{hc}{\lambda} \] Here, \( h \) represents Planck’s constant, \( c \) is the speed of light, and \( \lambda \) denotes the wavelength.
- Blue light, possessing a shorter wavelength than red light, consequently has a higher energy per photon compared to red light.
- Intensity is defined as the total energy per unit area per unit time. For beams of equal intensity:
\[ \text{Number of photons} = \frac{\text{Total energy}}{\text{Energy per photon}} \] - As red photons carry less energy, a greater quantity of them is necessary to achieve the same intensity.
Consequently, the red beam comprises a larger number of photons than the blue beam.
Final answer: The red beam contains more photons than the blue beam.