what is the wavelength of an X- ray photon with energy 10 keV?(10,000eV)? what is the frequency?
Well, well, well! We have an X-ray enthusiast over here! Now, let me put my scientific clown nose on and take a shot at answering your question.
To find the wavelength of an X-ray photon, we can use the equation:
wavelength = h / (E * c)
Where:
wavelength is the wavelength of the photon,
h is Planck's constant (approximately 6.626 x 10^-34 J*s),
E is the energy of the photon (in this case, 10,000 eV converted to joules),
and c is the speed of light (approximately 3 x 10^8 m/s).
Plugging in the values, let's get cracking:
wavelength = (6.626 x 10^-34 J*s) / (10,000 eV * 1.602 x 10^-19 J/eV * 3 x 10^8 m/s)
Get your math gears ready! After crunching those numbers, the wavelength of the X-ray photon comes out to be approximately 0.124 nm (or 1.24 x 10^-10 meters).
Now, for frequency, we can use another equation:
frequency = E / h
Plugging in the values again, let's have some fun:
frequency = (10,000 eV * 1.602 x 10^-19 J/eV) / (6.626 x 10^-34 J*s)
Doing the math, we find that the frequency of our X-ray photon is about 1.518 x 10^18 Hz (or 1.518 exahertz).
Keep in mind that these values are just approximate, so don't take them too seriously! But hey, I hope I managed to inject a bit of humor into your scientific endeavors!
To calculate the wavelength of an X-ray photon with energy 10 keV (10,000 eV), you can use the equation:
λ = hc/E
Where:
λ is the wavelength
h is the Planck's constant (6.63 x 10^-34 J⋅s)
c is the speed of light (3 x 10^8 m/s)
E is the energy of the photon
Step 1: Convert the energy from eV to joules:
Given energy = 10,000 eV
1 eV = 1.6 x 10^-19 J (conversion factor)
Energy (E) = 10,000 eV x (1.6 x 10^-19 J/eV)
= 1.6 x 10^-15 J
Step 2: Substitute the values into the equation:
λ = (6.63 x 10^-34 J⋅s) x (3 x 10^8 m/s) / (1.6 x 10^-15 J)
≈ 1.24 x 10^-10 m
Therefore, the wavelength of an X-ray photon with an energy of 10 keV is approximately 1.24 x 10^-10 meters (or 124 picometers).
To calculate the frequency, you can use the equation:
f = E/h
Where:
f is the frequency
E is the energy of the photon
h is the Planck's constant
Step 3: Substitute the values into the equation:
f = (1.6 x 10^-15 J) / (6.63 x 10^-34 J⋅s)
≈ 2.42 x 10^18 Hz
Therefore, the frequency of the X-ray photon is approximately 2.42 x 10^18 Hz (or 2.42 exahertz).
To find the wavelength of an X-ray photon, you can use the equation that relates the energy of a photon (E) to its wavelength (λ) and frequency (ν):
E = hν
where h is Planck's constant (6.626 x 10^(-34) J⋅s), ν is the frequency, and c is the speed of light in a vacuum (3 x 10^8 m/s).
First, let's convert the energy from keV to joules. 1 keV is equal to 1.6 x 10^(-19) Joules.
Given that the energy is 10 keV, we can calculate the energy in joules:
E = 10,000 eV * (1.6 x 10^(-19) J/eV) = 1.6 x 10^(-15) J
Now, using the equation E = hν, we can solve for frequency:
ν = E / h = (1.6 x 10^(-15) J) / (6.626 x 10^(-34) J⋅s) = 2.42 x 10^18 Hz
Finally, to find the wavelength, we can use the equation that relates the frequency and wavelength of electromagnetic waves:
c = λν
Rearranging the equation to solve for wavelength:
λ = c / ν = (3 x 10^8 m/s) / (2.42 x 10^18 Hz) = 1.24 x 10^(-10) m
Therefore, the wavelength of an X-ray photon with energy 10 keV is approximately 1.24 x 10^(-10) meters (or 0.124 nanometers), and the frequency is approximately 2.42 x 10^18 Hz.
h*c/(wavelength) = E
= 10^4 eV*1.6*10^-19 J/eV
= 1.6*10^-15 J
You know what h and c are. Solve for the wavelength.
Wavelength = h*c/E
= 6.62*10^-34*3*10^8/1.6*10^-15
= 1.25*10^-10 m
= 0.125 nm = 1.25 Angstroms
The frequency is c/(wavelength)