How many photons with a wavelength of 450 nm is required to have mass of 1.25 micrograms?

Question

How many photons with a wavelength of 450 nm is required to have mass of 1.25 micrograms?

Answer 1

I didn't know photons had a mass. What does violet light weigh? or red light?

Answer 2

I know, I don't understand. I don't know violet light or red light either, we haven't learned mass of those.

Answer 3

Explain why you would make one of the addendds a tens number when solving an addiction problem

Answer 4

To determine the number of photons required to have a specific mass, we need to use the equation E = mc², where E represents energy, m represents mass, and c represents the speed of light.

However, photons do not have rest mass. Instead, they have energy that is proportional to their frequency or inversely proportional to their wavelength. The energy of a single photon can be described by the equation E = hf, where E represents energy, h is Planck's constant (6.626 x 10^-34 J∙s), and f represents frequency.

Since the energy of an individual photon can be calculated, we can then calculate the number of photons required to have a specific mass.

First, we need to convert the given mass of 1.25 micrograms to kilograms (1 microgram = 1 x 10^-9 kg). Therefore, the mass becomes 1.25 x 10^-15 kg.

Next, we can calculate the energy of a single photon using its wavelength and the speed of light. The energy of a photon can be expressed as E = hc/λ, where 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.

Plugging in the values, we get:
E = (6.626 x 10^-34 J∙s) * (3 x 10^8 m/s) / (450 x 10^-9 m).

Calculating this expression, we find that the energy of a single photon with a wavelength of 450 nm is approximately 1.473 x 10^-19 J.

Now, to find the number of photons required to achieve a mass of 1.25 micrograms, we need to divide the given mass by the energy of a single photon:

Number of photons = (Mass) / (Energy of a single photon)
= (1.25 x 10^-15 kg) / (1.473 x 10^-19 J)

Performing this calculation, we find that it would require approximately 8.479 x 10^3 photons with a wavelength of 450 nm to have a mass of 1.25 micrograms.