Two sources produce electromagnetic waves. source b produces a wavelength that is three times the wavelength produced by source a. each photon from source a has an energy of 2.1*10^-18 j. what is the energy of a photon from source b?

Explanation:

1) Key concepts and notation

For this case we can use the Einstein's formula for the energy of a photon. The original formula from Einstein's is:

Also Planck's find and equation for the energy of a photon, given by:

representing the Planck's constant

f= the frequency

Based on the above formula, the energy of a photon depends only on its wavelength and frequency. The energy is proportional to (given from the problem).

2) Formulas to apply

The following relationship is important:

  (1)

Where is the speed of the light

Solving f from equation (1) we got

  (2)

3) Apply the formulas

We can find the energy for each source on the following way:

Replacing the value given, we got:

  (3)

After this solving for from equation (3) we got:

  (4)

Similarly for the energy source B we have:

  (5)

For the next step we can apply the condition given, and we got:   (6)

Replacing the condition on equation (6) into equation (5):

  (7)

And now, we can replace equation (4) into equation (7):

  (7)

So the final answer would be .