Find the frequency and wavelength of a 50-MeV gamma-ray photon.
Well, aren't you full of energy! A 50-MeV gamma-ray photon has a frequency that can be calculated using Einstein's famous equation, E = hf, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency. So, rearranging the equation, we have f = E/h.
Now, let's plug in the numbers! Converting the energy of the photon to joules gives us 50 MeV x (1.602 x 10^-13 J/1 MeV) = 8.01 x 10^-12 J. Dividing this by Planck's constant, we get a frequency of approximately 1.2105 x 10^20 Hz.
As for the wavelength, we can use the relationship between frequency and wavelength, c = fλ, where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength. Rearranging this equation gives us λ = c/f.
Plugging in the numbers again, we have λ = (3 x 10^8 m/s)/(1.2105 x 10^20 Hz), which gives us a wavelength of approximately 2.47 x 10^-12 meters.
So, the frequency of your energetic gamma-ray photon is approximately 1.2105 x 10^20 Hz, and its wavelength is approximately 2.47 x 10^-12 meters. Just don't let it go to its head!
To find the frequency and wavelength of a gamma-ray photon with an energy of 50 MeV, we can use the relationship between energy, frequency, and wavelength.
The energy of a photon can be calculated using 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 photon.
First, let's convert the energy of the photon from MeV to joules:
1 MeV = 1.602 x 10^-13 J
So, 50 MeV is equal to:
50 MeV x 1.602 x 10^-13 J/MeV = 8.01 x 10^-12 J
Next, we can rearrange the equation to solve for frequency:
f = E / h
Plugging in the values, we get:
f = 8.01 x 10^-12 J / (6.626 x 10^-34 J.s)
Calculating the frequency gives us:
f ≈ 1.21 x 10^22 Hz
To find the wavelength, we can use the equation:
c = λf
Where c is the speed of light (3 x 10^8 m/s), λ is the wavelength, and f is the frequency.
Rearranging the equation to solve for wavelength:
λ = c / f
Plugging in the values:
λ = (3 x 10^8 m/s) / (1.21 x 10^22 Hz)
Calculating the wavelength gives us:
λ ≈ 2.48 x 10^-14 m
Therefore, the frequency of the 50-MeV gamma-ray photon is approximately 1.21 x 10^22 Hz and the wavelength is approximately 2.48 x 10^-14 m.
To find the frequency and wavelength of a photon, we can 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 photon.
First, let's convert the energy of the photon from MeV to Joules. We can use the conversion factor:
1 MeV = 1.602 × 10^(-13) Joules
So for a 50-MeV photon:
Energy (E) = 50 MeV * (1.602 × 10^(-13) Joules/1 MeV) = 8.01 × 10^(-12) Joules
Now we can rearrange the equation to solve for frequency:
f = E / h
Planck's constant (h) is approximately 6.626 × 10^(-34) Joule-seconds.
f = (8.01 × 10^(-12) Joules) / (6.626 × 10^(-34) Joule-seconds)
Calculating this gives us:
f ≈ 1.21 × 10^22 Hz
Finally, we can use the equation:
c = λf
Where c is the speed of light and λ is the wavelength.
The speed of light (c) is approximately 3 × 10^8 meters per second.
λ = c / f
λ = (3 × 10^8 meters per second) / (1.21 × 10^22 Hz)
Calculating this gives us:
λ ≈ 2.48 × 10^(-15) meters
Therefore, the frequency of a 50-MeV gamma-ray photon is approximately 1.21 × 10^22 Hz and its wavelength is approximately 2.48 × 10^(-15) meters.