Question

Radio waves are typically used for communication because they have such low energy, and thus won't hurt living objects when they come in contact with them. A radio wave has a wavelength of 0.344 m. What is the energy of one photon of this radiation?

Your answer will be on the order of ~ x10-25 J. Please give the answer as a whole number that would be multiplied by x10-25. I.e. if the answer is 2.20x10-25J, please answer as 2.20

Answer 1

Expressed as a function of x10^-25, E = 578 J, to 3 sig figs

Step-by-step explanation:

E=hv

where

E is energy, in Joules

h is Plank's constant of 6.626x10^-34 J-s

and v is frequency, in s^-1

We are given wavelength (0.344 m), but need frequency (s^-1). Use the relationship:

c = wv, where c is the speed of light and w is wavelength.

3x10^6 m/s = (0.344 m)*v

v = 8720930 or 8.721x10^6 s^-1

Now we can calculate E:

E = (6.626x10^-34 J-s)*(8.721x10^6 s^-1)

E = 5.778 x 10^-27 J

Expressed as a function of x10^-25, this is

E = 578 J, to 3 sig figs

[The wavelength0.344 meters seems high, but it provides an answer close to that predicted in the question. Electromagnetic waves are generally expressed in nanometers, not m. So this must be a very low energy signal.