A 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 600 nm, so make the simplifying assumption that all the light has this wavelength. How many visible-light photons does the bulb emit per second?

검증된 단계별 안내

Step 1: Start by calculating the energy of a single photon using the formula \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J·s} \)), \( c \) is the speed of light (\( 3.00 \times 10^8 \, \text{m/s} \)), and \( \lambda \) is the wavelength of the light (600 nm or \( 600 \times 10^{-9} \, \text{m} \)).

Step 2: Substitute the given values into the formula \( E = \frac{hc}{\lambda} \) to calculate the energy of a single photon. Ensure that the wavelength is converted to meters before substituting.

Step 3: Determine the total energy emitted as visible light per second. This is given as 5 W, which means 5 joules of energy are emitted per second.

Step 4: Calculate the number of photons emitted per second by dividing the total energy emitted as visible light per second by the energy of a single photon. Use the formula \( N = \frac{P}{E} \), where \( P \) is the power of visible light (5 W) and \( E \) is the energy of a single photon.

Step 5: Simplify the expression to find the number of photons emitted per second. Ensure that the units are consistent throughout the calculation (e.g., joules for energy).

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주요 개념

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Photon Energy

The energy of a photon is determined by its wavelength, given by the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength in meters. For visible light at 600 nm, this relationship allows us to calculate the energy of each photon emitted by the lightbulb.

Power and Energy Relationship

Power is defined as the rate at which energy is transferred or converted, measured in watts (W). In this context, the lightbulb emits 5 W of visible light, meaning it produces 5 joules of energy per second. This relationship is crucial for determining how many photons are emitted based on the energy each photon carries.

Calculating Photon Emission Rate

To find the number of photons emitted per second, divide the total power output in visible light (5 W) by the energy of a single photon. This calculation provides the photon emission rate, which is essential for understanding the light output of the bulb in terms of individual photons.