Question

A local AM radio station broadcasts at an energy of (4.15 X 10^31) kJ/photon. Calculate the frequency at which it is broadcasting. Frequency = KHz (1 KHz = (10^3) sec(^1))

a) (4.15 X 10^28) KHz
b) (4.15 X 10^34) KHz
c) (4.15 X 10^25) KHz
d) (4.15 X 10^22) KHz

Answer 1

Using Planck's equation and the provided energy, we calculated the frequency of the radio station's broadcast to be approximately 6.26 x 10^64 KHz, which does not match any of the provided options.

Step-by-step explanation:

To calculate the frequency of the radio station's broadcast, we can use the energy of a photon and the Planck's equation E = h⋅ν, where E is the energy of the photon in joules, h is Planck's constant (6.626 x 10-34 J⋅s), and ν (nu) is the frequency in hertz (Hz).

First, let's convert the given energy from kilojoules to joules.

(4.15 x 1031) kJ/photon = (4.15 x 1031 x 103) J/photon = 4.15 x 1034 J/photon

Now, using Planck's equation:

E = h⋅ν
ν = E / h
ν = (4.15 x 1034 J/photon) / (6.626 x 10-34 J⋅s)
ν = 6.26 x 1067 s-1

To convert this to kilohertz (KHz), we divide by 103:

ν = 6.26 x 1067 s-1 / 103
ν = 6.26 x 1064 KHz

Looking at the options provided by the student, none of them match the calculated value.