A cathode ray tube operates at 80 kV with a current of 875 uA. Calculate the
a)Intesity (# of photons per second f the x-rays
b)Minimum wavelength of the x-rays produced by the CRT
thanks in advance
a) To my knowledge each CRT electron does not necessarily produce 1 X-ray photon. The question cannot be answered with the information given
b) The X-ray photon can have no more energy that the electron striking the cathode, and you know what that is:
E = e*V = 80,000 V * 1.6*10-19 J/V
Use that energy and E > hc/(wavelength) to get the minimum wavelength.
I typed exactly what is said on the question sheet.
Answer given is 5.47*10^15 photons/s
As each photon strikes the electron, it is absorbed and then any excess energy is then re-radiated in the form of x-rays, from what i understand, i need to find the remaining energy (since i know energy of electron after using current, t=1.0s and q(charge)=1.60*10^-19c)
And intensity can be figured out by using
E=nhf
E=n(#of photons)h(planks constant, i think its the J per s[6.63*10^-34J.s])f frequencey (which i don't have, this is where im stuck)
My classmate figured it out and I will attempt to retrieve the procedure from him, thanks anyway.
In a CRT, photons do not strike electrons to produce X-rays. Electrons strike metal atoms to liberate photons. The deceleration/excitation process produces both continuum and atomic line radiation. There can be more one photon produced per electron.
Getting agreement with 'book' or 'question sheet' answers does not always mean the book is right, or that the course is being properly taught.
huh....
To calculate the intensity of the X-rays produced by the cathode ray tube (CRT), we need to use the equation:
Intensity = Number of photons per second / Area
To calculate the number of photons per second, we need to use the equation:
Number of photons per second = Current / Charge of one electron
To calculate the area, we can assume it to be the surface area of a sphere with a radius of 1 meter, as an approximation.
a) Calculating the intensity of X-rays:
Step 1: Calculate the charge of one electron.
The charge of one electron is approximately 1.6 x 10^-19 Coulombs.
Step 2: Calculate the number of photons per second.
Number of photons per second = Current / Charge of one electron
= 875 x 10^-6 A / (1.6 x 10^-19 C)
Step 3: Calculate the area.
Area = 4πr^2
= 4 x π x (1 m)^2
Step 4: Calculate the intensity.
Intensity = Number of photons per second / Area
b) Calculating the minimum wavelength of X-rays:
To calculate the minimum wavelength of the X-rays produced by the CRT, we can use the equation known as the "Bragg equation":
2d sin(θ) = nλ
Where:
- d is the spacing between the planes of the crystal.
- θ is the angle of incidence.
- n is an integer representing the order of the X-ray diffraction.
- λ is the wavelength of X-rays.
In the case of a CRT, we assume that a crystal with interplanar spacing of 1 Å (Angstrom) is used for diffraction. Therefore, d = 1 x 10^-10 m.
We also assume n = 1, as we are considering the first-order diffraction.
Step 1: Calculate the value of sin(θ).
The value of sin(θ) can be determined using the equation:
sin(θ) = λ / (2d)
Step 2: Substitute the known values to solve for the wavelength.
λ = 2d sin(θ)
Given that θ = 90° (as we are considering the maximum diffraction angle), substitute this value into the equation above to calculate the minimum wavelength.