Question

What is the wavelength of a radio photon from an "AM" radio station that broadcasts at 1520 kilohertz? And what is its energy?

Answer 1

Given parameters:

Frequency of the wave  = 1520kHz   = 1520 x 10³Hz

Unknown:

Wavelength of the radio photon = ?

Energy of the wave = ?

Solution:

The wavelength of any electromagnetic wave can found using the expression below;

          C = f x ∧

Where C is the velocity of light  = 3 x 10⁸m/s

            f is the frequency of the wave

            ∧ is the wavelength

Since the unknown is ∧, input the known parameters and solve for it;

       3 x 10⁸  = 1520 x 10³  x ∧

    Wavelength  = $\frac{3 x 10^{8} }{1520 x 10^{3} }$  

   Wavelength  = $\frac{3 x 10^{8} }{1.52 x 10^{6} }$

  Wavelength  = 1.97 x 10²m

ii. Energy of the wave;

        Energy of a wave  = hf

where h is the planck's constant = 6.63 x 10⁻³⁴ J Hz⁻¹

           f is the frequency of the wave

Input the parameters and solve;

            Energy of the wave = 6.63 x 10⁻³⁴ x 1.52 x 10⁶

                                               = 10.1 x 10⁻²⁸J

The energy of this wave is 10.1 x 10⁻²⁸J