Question

Find the energy in joules and eV of photons in radio waves from an FM station that has a 90.0-MHz broadcast frequency.

a. (2.21 × 10⁻²⁴) J, (1.38 × 10⁻¹⁷) eV
b. (2.21 × 10⁻¹⁴) J, (1.38 × 10⁻⁹) eV
c. (2.21 × 10⁻²⁴) J, (1.38 × 10⁻⁹) eV
d. (2.21 × 10⁻¹⁴) J, (1.38 × 10⁻¹⁷) eV

Answer 1

To find the energy of photons in radio waves, we use the equation E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the radio wave. The energy in joules is (2.21 × 10^-14) J and the energy in electron volts (eV) is (1.38 × 10^-17) eV.

Step-by-step explanation:

To find the energy of photons in radio waves, we can use the equation:

E = hf

where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the radio wave.

To convert the frequency from MHz to Hz, we multiply by 10^6. So, the frequency of the radio wave in Hz is 90.0 x 10^6 Hz.

Substituting these values into the equation, we get:

E = (6.626 x 10^-34 J·s) × (90.0 x 10^6 Hz)

Simplifying this expression gives us the energy in joules. To convert the energy from joules to electron volts (eV), we can use the conversion factor 1 eV = 1.602 x 10^-19 J.

Multiplying the energy in joules by this conversion factor will give us the energy in eV.

Therefore, the correct answer is (2.21 × 10^-14) J, (1.38 × 10^-17) eV.