One watt (W) is equal to 1 J/s. Assuming that 5.0% of the energy output of a 75 W light bulb is visible light and that the average wavelength of the light is 550 nm, how many photons are emitted by the light bulb each second?

Verified step by step guidance

1. Convert the power of the light bulb to energy per second: 75 W = 75 J/s.
2. Calculate the energy output in visible light: 5.0% of 75 J/s.
3. Use the energy of a photon formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength (550 nm).
4. Convert the wavelength from nanometers to meters for use in the formula.
5. Divide the total energy output in visible light by the energy of a single photon to find the number of photons emitted per second.

Key Concepts

Energy and Power

Power is the rate at which energy is transferred or converted, measured in watts (W), where 1 W equals 1 joule per second (J/s). In this context, the light bulb's power rating indicates how much energy it consumes per second, which is crucial for calculating the total energy output in visible light.

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, c is the speed of light, and λ is the wavelength. For light with a wavelength of 550 nm, this relationship allows us to calculate the energy of each emitted photon, which is essential for determining the total number of photons emitted.

Calculating Photon Emission

To find the number of photons emitted per second, we first calculate the total energy output in visible light by multiplying the power of the bulb by the percentage of energy that is visible. Then, we divide this energy by the energy of a single photon to determine how many photons are emitted each second, linking energy output to photon count.