(a) What is the frequency of a photon whose energy is 3.5 times the rest energy of an electron? (b) What would be the linear momentum of the photon?
ε = 3•mc^2= hν,
=> ν =3•mc^2/h =
= 3•9.1•10^-31•(3•10^8)^2/6.63•10^-34 =
= 3.7•10^20 Hz.
p= ε /c =3•mc^2/c =3•mc = 3•9.10^-31•3•10^8 =8.2•10^-22 kg•m/s.
To determine the frequency of a photon whose energy is 3.5 times the rest energy of an electron, you need to use the equation that relates energy and frequency for photons, known as Planck's equation:
E = hf
where E is the energy of the photon, h is Planck's constant (approximately 6.626 x 10^-34 J · s), and f is the frequency of the photon.
Since the energy of the photon is given as 3.5 times the rest energy of an electron, we can write the equation as:
E = 3.5 x rest energy of electron
To find the frequency, we can rearrange the equation as:
f = E / h
Substituting the given values, we have:
f = (3.5 x rest energy of electron) / h
Now, let's find the rest energy of an electron, which is given by Einstein's famous equation:
E = mc^2
where E is the energy, m is the mass of the electron, and c is the speed of light (approximately 3 x 10^8 m/s).
The rest mass of an electron is approximately 9.109 x 10^-31 kg. Plugging this into the equation, we have:
E = (9.109 x 10^-31 kg)(3 x 10^8 m/s)^2
Simplifying the equation, we get:
E = 8.187 x 10^-14 J
Now we can substitute the value of the rest energy of the electron into the equation we derived earlier:
f = (3.5 x 8.187 x 10^-14 J) / (6.626 x 10^-34 J · s)
After calculating the result, we obtain the frequency of the photon.
To determine the linear momentum of the photon, we can use the equation relating momentum and frequency for photons, known as de Broglie's equation:
p = hf / c
where p is the linear momentum of the photon and c is the speed of light.
By substituting the calculated value of the frequency into the equation, we can determine the linear momentum of the photon.