Question

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

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

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.

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.

Key concepts

Intensity of Light

Intensity of light refers to how much energy a light beam carries over a certain area per time unit. It's crucial to understand that intensity is not dependent on the speed or energy per photon but rather on the overall amount of photons striking a surface.

When you increase the intensity of a light beam while keeping its frequency constant, you are effectively increasing the number of photons hitting a surface per second. This is because the energy per photon is solely dependent on frequency, and intensity scales with the number of photons. Hence, if intensity increases, more photons are being delivered in the same timeframe.

• A simple analogy to grasp this is to imagine a hose releasing water droplets: increasing the intensity is like increasing the flow rate, hence more droplets (photons) are released, but the size (energy per photon) remains the same based on the "nozzle setting" (frequency).

Photon Energy

Understanding photon energy is key in discussing light and its properties. Photon energy is defined by the equation \( E = h \times f \), where \( E \) is energy, \( h \) is Planck's constant, and \( f \) is the frequency of the light. It's important to note that photon energy is entirely dependent on frequency. If the frequency is unchanged, the energy per photon is unchanged, regardless of the intensity of the light beam.

To reiterate, increasing the intensity does not affect individual photon energy. One can think of each photon as a "packet" or "particle" of energy; increasing their number means increasing light overall brightness, not the energy in each packet.

• Thus, if you double the intensity with a constant frequency, you're not doubling the photon energy; you are doubling the number of photons.
• This distinction helps prevent misunderstanding that intensity affects energy per photon.

Wavelength and Frequency

Wavelength and frequency are inherently linked through the equation \( \lambda = c / f \). Here, \( \lambda \) is the wavelength, \( c \) is the speed of light, and \( f \) is the frequency. This relationship highlights how wavelength shortens with higher frequencies and lengthens with lower frequencies.

If frequency is held constant, wavelength remains unchanged, no matter the intensity change. Wavelength determination is vital as different wavelengths within visible light represent different colors, affecting the light's perception.

• An important point to remember is that the speed of light \( c \) remains constant in a vacuum, underscoring the unchanging nature of \( \lambda \) when \( f \) is constant.
• Therefore, in a classroom, a fixed-frequency laser pointer keeps its color (wavelength) no matter how bright (intense) it gets.

Planck's Constant

Planck's constant, denoted as \( h \), is a fundamental physical constant that plays a pivotal role in quantum mechanics, especially in determining photon energy. It is approximately \( 6.626 \times 10^{-34} \) J·s and acts as a proportionality factor in the equation \( E = h \times f \).

Planck's constant links the energy \( E \) of a photon to its frequency \( f \), highlighting how energy transitions occur at quantum scales. This constant is essential in modern physics as it underpins the concept of quantization, where physical properties, like energy, can be discrete rather than continuous.

• For students, appreciating Planck's constant helps in understanding the revolutionary shift from classical to quantum physics. It shows how statements like "light acts as both particle and wave" are rooted scientifically.
• The constancy of \( h \) assures consistent calculations in photon energy, critical when exploring phenomena like the photoelectric effect and atomic emissions.