How many photons can a 100 W lamp generate in 36 seconds?

Question:

A 100 W lamp emits yellow light of wavelength 583 nm. How many photons can the lamp generate in 36 seconds?

Answer:

To find the number of photons emitted by a 100 W lamp in 36 seconds, we need to calculate the energy per photon and use it to determine the number of photons using the formula (Power × time) / Energy per photon.

A 100 W lamp emitting yellow light with a wavelength of 583 nm generates a certain number of photons in a given time frame. In this case, we are looking to find out how many photons are produced in 36 seconds.

To calculate this, we first need to determine the energy per photon by using the formula E = nhc/λ, where E represents the energy, n is the number of photons, h is Planck's constant, c is the speed of light, and λ is the wavelength. Since the lamp emits yellow light with a wavelength of 583 nm, we can plug in the values and calculate the energy per photon.

Next, we can use the formula (Power × time) / Energy per photon to find the number of photons emitted in 36 seconds. The power emitted in visible light production by the 100 W lamp is 10.0% of 100 W, which is 10.0 J/s. By substituting this power value, the time of 36 seconds, and the energy per photon into the formula, we can determine the total number of photons generated by the lamp within the given time frame.

By following these calculations, we will be able to find out the exact number of photons that a 100 W lamp can produce in 36 seconds. Understanding the energy per photon and applying the correct formulas will lead us to the final answer.