Waves and energy

1. Question: Calculate the energy in keV of an x-ray photon that has a wavelength of 0.05 nm.
2. Question: A popular radio station broadcasts at 100 MHZ. Calculate the wavelength of this frequency

Answer:

1. Question: Calculate the energy in keV of an x-ray photon that has a wavelength of 0.05 nm.

Speed of the wave = frequency x wavelength
Wavelength (w) = Speed of the wave (c) /frequency (f)

Therefore using the formula:
Energy of photon = Planck's constant (h) x frequency of photon (f) = hc/w

So: Energy of photon = [6.63x10^-34 x 3x10⁸]/0.05x10^-9 = 4x10^-15 J

Now the energy is keV is that in Joules/1.6x10^-16 since 1keV = 1.6x10^-16 J

Therefore for our photon: Energy = 4x10^-15/1.6x10^-16 = 24.9 keV

2. Question: A popular radio station broadcasts at 100 MHZ. Calculate the wavelength of this frequency.

100 MHz = 100 000 000 Hz

Using the formula:

Speed of the wave = frequency x wavelength

Radio waves travel at the speed of light (300 000 000 m/s). So:

Wavelength = speed/frequency = 300 000 000/100 000 000 = 3 m