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Chapter 36: Problem 6

Which one of the following statements is true if the intensity of a light beam is increased while its frequency is kept the same? a) The photons gain higher speeds. b) The energy of the photons is increased. c) The number of photons per unit time is increased. d) The wavelength of the light is increased.

Short Answer

Expert verified
a) The speed of light increases. b) The energy of each individual photon increases. c) The number of photons per unit time is increased. d) The wavelength of the light increases. Answer: c) The number of photons per unit time is increased.

Step by step solution

01

Recall the properties of light

Light consists of particles called photons. The energy of a photon, E is given by the equation E = h * f, where h is the Planck's constant (approximately 6.626 x 10^-34 J·s) and f is the frequency of the light. The speed of light, c, is a universal constant (approximately 3 x 10^8 m/s) and applies to all photons. Wavelength, λ, and frequency are related by the equation λ=c/f, where λ is the wavelength and f is the frequency of the light. Lastly, intensity is proportional to the number of photons per unit time.
02

Evaluate the statements

a) The speed of light is a universal constant, and does not change. Therefore, this statement is false. b) The energy of a photon depends only on the frequency, E = h * f. Since the frequency remains the same, the energy of each individual photon does not increase. This statement is false. c) Increasing the intensity of a light beam is equivalent to increasing the number of photons per unit time. This statement is true. d) Wavelength and frequency are related by the equation λ = c/f. Since the frequency is kept the same, the wavelength of the light will not change. This statement is false. Based on our analysis, the correct answer is: c) The number of photons per unit time is increased.

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