U is the voltage between the anode and cathode, are you familiar with E = V×Q?
Thanks a lot! I wasn't familiar with it before but I am now that you have mentioned it! So how is the energy of electrons used for imaging connected to magnitude of the acceleration voltage between the anode and cathode of electron beam source. So I know it simply state in the text the relationship between these two but I dont quite understand what they are trying to explain here. I dont undretsand the content. What is this acceleration voltage and what causes it? Also, how do you go from to
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I really apologise for my dumb questions! I have done mechanics As level and got an A in that but other than that I am not very familiar with physics :/ - this is biophysics stuff for med school
E is energy. Equation is 'energy = charge x voltage'
Thanks a lot! I wasn't familiar with it before but I am now that you have mentioned it! So how is the energy of electrons used for imaging connected to magnitude of the acceleration voltage between the anode and cathode of electron beam source. So I know it simply state in the text the relationship between these two but I dont quite understand what they are trying to explain here. What is this acceleration voltage and what causes it? Also, how do you go from to
Attachment not found
I really apologise for my dumb questions! I have done mechanics As level and got an A in that but other than that I am not very familiar with physics :/ - this is biophysics stuff for med school
This may help ... The equation for wavelength is = h / momentum (p). Momentum depends on the ke, E: since E = 1/2 m v2, p = mv = sqrt(2mE) since E = q x voltage, they get an equation for wavelength (of electrons - this may be an odd concept if you've not done much physics!) depending on accelerating voltage (which they call U) I guess being able to change the wavelength of electrons is useful for electron microscopes. (btw they are giving the electrons ke by accelerating them towards a large +ve voltage)
This may help ... The equation for wavelength is = h / momentum (p). Momentum depends on the ke, E: since E = 1/2 m v2, p = mv = sqrt(2mE) since E = q x voltage, they get an equation for wavelength (of electrons - this may be an odd concept if you've not done much physics!) depending on accelerating voltage (which they call U) I guess being able to change the wavelength of electrons is useful for electron microscopes. (btw they are giving the electrons ke by accelerating them towards a large +ve voltage)
Thanks a lot! So I equated p=mv and p=sqrt(2mE) and rearranged and this gave me E = 1/2 mv^2. I also have to know that E = q x voltage but then how do you get equation for wavelength of electrons from there? Apologies again!
wavelength = h / p (de Broglie's equation - just accept it's true!) = h / (mv) = h / sqrt(2m E) (remember we know E = 1/2 m v2) = h / sqrt(2m qU) (E = qU) = numbers / sqrt(U) where numbers = h / sqrt(2mq). I trust them = 1.225 (x 10-9)
wavelength = h / p (de Broglie's equation - just accept it's true!) = h / (mv) = h / sqrt(2m E) (remember we know E = 1/2 m v2) = h / sqrt(2m qU) (E = qU) = numbers / sqrt(U) where numbers = h / sqrt(2mq). I trust them = 1.225 (x 10-9)
hope that's ok now.
Thank you very much! I didn't trust them so I tried to calculate it myself haha - sorry! just going to attach my workings in a few minutes - my laptop is constantly crashing for some reason Here it is :
Thanks a lot! I wasn't familiar with it before but I am now that you have mentioned it! So how is the energy of electrons used for imaging connected to magnitude of the acceleration voltage between the anode and cathode of electron beam source. So I know it simply state in the text the relationship between these two but I don’t quite understand what they are trying to explain here. I don’t understand the content. What is this acceleration voltage and what causes it?
You need some basic concepts of electric field.
Assume that there is a pair of metallic parallel plates separated by a distance d and is connected to a potential difference of say V. A uniform electric field E is set up between the pair of metallic parallel plates. When a stationary electron q is placed in just outside the negative potential plate, it is subjected to an electric force qE. So it would accelerate toward the positive potential plate.
From Newton’s 2nd law,
F = ma
qE = ma ---Eqn(1)
The uniform electric field between the pair of metallic parallel plates is “defined” by
E=dV ---Eqn(2)
Sub (2) into (1),
qdV=ma
qV = mad ---Eqn(3)
If you manipulate the left-hand side of (3) by
21×m(2ad)=21mv2=KE
where I have used v2 = u2 + 2as.
So we can say that the gain in KE of the electron is equal to qV.
Note that we can KE in terms of momentum of the electron:
Also, how do you go from to I really apologise for my dumb questions! I have done mechanics As level and got an A in that but other than that I am not very familiar with physics :/ - this is biophysics stuff for med school
λ=2mEh=2mqVh
h is known as the Planck constant, 6.63 × 10-34 m2 kg / s
charge on electron is not -1! ignore the sign - doesn't work well under sqrt! The equation has assumed electron is negative. q = 1.6 x 10-19 C. It worked for me
charge on electron is not -1! ignore the sign - doesn't work well under sqrt! The equation has assumed electron is negative. q = 1.6 x 10-19 C. It worked for me
Ah yes thank you very much Really appreciate your time!!
Assume that there is a pair of metallic parallel plates separated by a distance d and is connected to a potential difference of say V. A uniform electric field E is set up between the pair of metallic parallel plates. When a stationary electron q is placed in just outside the negative potential plate, it is subjected to an electric force qE. So it would accelerate toward the positive potential plate.
From Newton’s 2nd law,
F = ma
qE = ma ---Eqn(1)
The uniform electric field between the pair of metallic parallel plates is “defined” by
E=dV ---Eqn(2)
Sub (2) into (1),
qdV=ma
qV = mad ---Eqn(3)
If you manipulate the left-hand side of (3) by
21×m(2ad)=21mv2=KE
where I have used v2 = u2 + 2as.
So we can say that the gain in KE of the electron is equal to qV.
Note that we can KE in terms of momentum of the electron:
21mv2=21mm2v2=2mp2
λ=2mEh=2mqVh
h is known as the Planck constant, 6.63 × 10-34 m2 kg / s
Thank you so much! My brain is in sleep mode at the moment haha but I will definitely reply back to this and also to your kind reply back to my other question! Really appreciate your help
Thank you so much! My brain is in sleep mode at the moment haha but I will definitely reply back to this and also to your kind reply back to my other question! Really appreciate your help