Physics energy, current and electrical potential of particle accelerator 🎆
Hello, I have answered the question below but would like some advice on whether I can improve my answer or if anyone is able to check whether I have made any mistakes ?
A particle accelerator accelerates bunches of protons, each containing 115 billion particles, to an energy of 6.5 TeV (1 eV is the energy of one proton or electron that is accelerated by a potential of 1 Volt).
i. What is the electrical potential, in Volts, of each particle?
Is this the total energy divided by the total number of particles to find the energy per particle.
So, (6.5*10^12)/(115*10^9)=56.5eV per particle
Converting 56.5eV to V = 3.532608125 * 10^20 ~ 3.5*10^20 V
Or since the question states " 1 eV is the energy of one proton or electron that is accelerated by a potential of 1 Volt" does this mean that 6.5 TeV = 6.5*10^12 eV = 6.5*10^12 V ?
ii. If the proton charge is 1.6 * 10^(-19) C, what is the energy, in Joules, of each bunch?
6.5 TeV = 6.5*10^12 eV = 4.0625*10^31 V per bunch
W=V * Q
W= 4.0625*10^31* 1.6*10^-19
W= 6.5*10^12 J = 6.5*10^9 kJ
iii. If one bunch reaches the collision point every 25 ns, what is the average electric current, in Amps, due to these arriving bunches?
I = charge/time
I = (1.6*10^-19)/(2.5*10^8)
Current = 6.4 * 10^-12 A
I am really grateful to anyone who replies 😊
A particle accelerator accelerates bunches of protons, each containing 115 billion particles, to an energy of 6.5 TeV (1 eV is the energy of one proton or electron that is accelerated by a potential of 1 Volt).
i. What is the electrical potential, in Volts, of each particle?
Is this the total energy divided by the total number of particles to find the energy per particle.
So, (6.5*10^12)/(115*10^9)=56.5eV per particle
Converting 56.5eV to V = 3.532608125 * 10^20 ~ 3.5*10^20 V
Or since the question states " 1 eV is the energy of one proton or electron that is accelerated by a potential of 1 Volt" does this mean that 6.5 TeV = 6.5*10^12 eV = 6.5*10^12 V ?
ii. If the proton charge is 1.6 * 10^(-19) C, what is the energy, in Joules, of each bunch?
6.5 TeV = 6.5*10^12 eV = 4.0625*10^31 V per bunch
W=V * Q
W= 4.0625*10^31* 1.6*10^-19
W= 6.5*10^12 J = 6.5*10^9 kJ
iii. If one bunch reaches the collision point every 25 ns, what is the average electric current, in Amps, due to these arriving bunches?
I = charge/time
I = (1.6*10^-19)/(2.5*10^8)
Current = 6.4 * 10^-12 A
I am really grateful to anyone who replies 😊
The TeV figure for a particle accelerator relates to the energy of each charged particle - not the energy of all the particles in a bunch.
fwiw it's the energy of each charged particle that determines how interesting the collisions might be in terms of producing exotic new particles (e.g. Higgs boson) It's somewhat analogous to the photoelectric effect - you don't get any electrons liberated if the photon energy is insufficient - regardless of how many photons of that energy you use.
the particles are arranged into bunches containing large numbers of particles to increase the probability that an exotic particle is detected.
so for particles with a charge the magnitude of one elemental charge (like a proton) getting the potential from an energy in eV is straightforward
fwiw it's the energy of each charged particle that determines how interesting the collisions might be in terms of producing exotic new particles (e.g. Higgs boson) It's somewhat analogous to the photoelectric effect - you don't get any electrons liberated if the photon energy is insufficient - regardless of how many photons of that energy you use.
the particles are arranged into bunches containing large numbers of particles to increase the probability that an exotic particle is detected.
so for particles with a charge the magnitude of one elemental charge (like a proton) getting the potential from an energy in eV is straightforward
Original post by Joinedup
The TeV figure for a particle accelerator relates to the energy of each charged particle - not the energy of all the particles in a bunch.
fwiw it's the energy of each charged particle that determines how interesting the collisions might be in terms of producing exotic new particles (e.g. Higgs boson) It's somewhat analogous to the photoelectric effect - you don't get any electrons liberated if the photon energy is insufficient - regardless of how many photons of that energy you use.
the particles are arranged into bunches containing large numbers of particles to increase the probability that an exotic particle is detected.
so for particles with a charge the magnitude of one elemental charge (like a proton) getting the potential from an energy in eV is straightforward
fwiw it's the energy of each charged particle that determines how interesting the collisions might be in terms of producing exotic new particles (e.g. Higgs boson) It's somewhat analogous to the photoelectric effect - you don't get any electrons liberated if the photon energy is insufficient - regardless of how many photons of that energy you use.
the particles are arranged into bunches containing large numbers of particles to increase the probability that an exotic particle is detected.
so for particles with a charge the magnitude of one elemental charge (like a proton) getting the potential from an energy in eV is straightforward
Thank you for your reply.
i. So if the TeV figure relates to the energy of each charged particle, would I just convert from TeV to eV, then eV to V to find the electrical potential, in Volts, of each particle?
So 6.5 TeV = 6.5 *10^12 eV
Then eV to V using the formula:
V(V)=1.602176565×10-^-19*E(eV)/Q(C)
The voltage V in volts (V) is equal to 1.602176565×10^-19 times the energy E in electron-volts (eV), divided by the electrical charge Q in coulombs (C):
V= 1.602176565×10^-19 * 6.5 *10^12/ 1.602176565×10^-19
V= 6,500,000,000,000 or 6.5 *10^12 V ?
Are parts ii and iii correct? 😊
Original post by Joinedup
The TeV figure for a particle accelerator relates to the energy of each charged particle - not the energy of all the particles in a bunch.
fwiw it's the energy of each charged particle that determines how interesting the collisions might be in terms of producing exotic new particles (e.g. Higgs boson) It's somewhat analogous to the photoelectric effect - you don't get any electrons liberated if the photon energy is insufficient - regardless of how many photons of that energy you use.
the particles are arranged into bunches containing large numbers of particles to increase the probability that an exotic particle is detected.
so for particles with a charge the magnitude of one elemental charge (like a proton) getting the potential from an energy in eV is straightforward
fwiw it's the energy of each charged particle that determines how interesting the collisions might be in terms of producing exotic new particles (e.g. Higgs boson) It's somewhat analogous to the photoelectric effect - you don't get any electrons liberated if the photon energy is insufficient - regardless of how many photons of that energy you use.
the particles are arranged into bunches containing large numbers of particles to increase the probability that an exotic particle is detected.
so for particles with a charge the magnitude of one elemental charge (like a proton) getting the potential from an energy in eV is straightforward
@Joinedup
Sorry I am still a bit confused so would my amended answer for i. be correct? And are parts ii and iii correct? 😊👍
i. 6.5 TeV = 6.5 *10^12 eV
Then eV to V using the formula:
V(V)=1.602176565×10-^-19*E(eV)/Q(C)
The voltage V in volts (V) is equal to 1.602176565×10^-19 times the energy E in electron-volts (eV), divided by the electrical charge Q in coulombs (C):
V= 1.602176565×10^-19 * 6.5 *10^12/ 1.602176565×10^-19
V= 6,500,000,000,000 or 6.5 *10^12 V ?
Hello, sorry I am still a little confused could someone please offer some help? See my amended answer and workings in the previous post😁
Original post by LukeWatson4590
Hello, sorry I am still a little confused could someone please offer some help? See my amended answer and workings in the previous post😁
Yeah that's correct - but you've convoluted the working second time round
The definition of an electronVolt is the change in energy needed to change the particles potential by 1 Volt
for particles with a charge the size of the charge of one electron (like a proton) it's a straight 1:1 relationship between potential in V and energy in eV
6.5TeV protons have a potential of 6.5TV
--
one Volt is defined as one Joule per Coulomb
the size of the charge on an electron is
1.602E-19 Coloumbs
so one eV is equal to 1.602E-19 Joules
and you've got 115E9 particles with 6TeV energy each
--
the charge on a proton is 1.602E-19 Coulombs
so each bunch of 115E9 protons has a charge of 115E9 * 1.602E-19
1.84E-8 Coulombs
if a bunch passes a point every 25E-9 s
then in one second 4.0E7 bunches pass
the Amp is defined as 1 Coulomb per second passing a point
so you'd multiply the charge of a bunch of protons by the number of bunches passing per second
Original post by Joinedup
Yeah that's correct - but you've convoluted the working second time round
The definition of an electronVolt is the change in energy needed to change the particles potential by 1 Volt
for particles with a charge the size of the charge of one electron (like a proton) it's a straight 1:1 relationship between potential in V and energy in eV
6.5TeV protons have a potential of 6.5TV
--
one Volt is defined as one Joule per Coulomb
the size of the charge on an electron is
1.602E-19 Coloumbs
so one eV is equal to 1.602E-19 Joules
and you've got 115E9 particles with 6TeV energy each
--
the charge on a proton is 1.602E-19 Coulombs
so each bunch of 115E9 protons has a charge of 115E9 * 1.602E-19
1.84E-8 Coulombs
if a bunch passes a point every 25E-9 s
then in one second 4.0E7 bunches pass
the Amp is defined as 1 Coulomb per second passing a point
so you'd multiply the charge of a bunch of protons by the number of bunches passing per second
The definition of an electronVolt is the change in energy needed to change the particles potential by 1 Volt
for particles with a charge the size of the charge of one electron (like a proton) it's a straight 1:1 relationship between potential in V and energy in eV
6.5TeV protons have a potential of 6.5TV
--
one Volt is defined as one Joule per Coulomb
the size of the charge on an electron is
1.602E-19 Coloumbs
so one eV is equal to 1.602E-19 Joules
and you've got 115E9 particles with 6TeV energy each
--
the charge on a proton is 1.602E-19 Coulombs
so each bunch of 115E9 protons has a charge of 115E9 * 1.602E-19
1.84E-8 Coulombs
if a bunch passes a point every 25E-9 s
then in one second 4.0E7 bunches pass
the Amp is defined as 1 Coulomb per second passing a point
so you'd multiply the charge of a bunch of protons by the number of bunches passing per second
Thank you for your reply and further detailed explanation I truly appreciate it. I have tried to correct my solutions and have attached them below.
So for i. since 1 V = 1eV in a 1:1 relationship as you state;
6.5 TeV = 6.5 TV = 6.5 *10^12V?
ii. W=V * Q
Q=(115*10^9)*(1.602*10^-19)=1.8423*10^-8
W=(6.5 *10^12)*(1.84*10^-8)
W=119,749.5 J
iii. As you have shown in one second 4.0 ^ 10^7 bunches reach the collision point. The charge on a bunch of protons was earlier shown as 1.8423*10^-8 C.
So ( 4.0 ^ 10^7)*(1.8423*10^-8)=0.73692 A
Can I just check that I should multiply the charge of a bunch of protons by the number of bunches passing per second to find the average electric current, since surely this contradicts the formula I = Q/t ?
Thank you very much again 👍
Original post by Joinedup
Yeah that's correct - but you've convoluted the working second time round
The definition of an electronVolt is the change in energy needed to change the particles potential by 1 Volt
for particles with a charge the size of the charge of one electron (like a proton) it's a straight 1:1 relationship between potential in V and energy in eV
6.5TeV protons have a potential of 6.5TV
--
one Volt is defined as one Joule per Coulomb
the size of the charge on an electron is
1.602E-19 Coloumbs
so one eV is equal to 1.602E-19 Joules
and you've got 115E9 particles with 6TeV energy each
--
the charge on a proton is 1.602E-19 Coulombs
so each bunch of 115E9 protons has a charge of 115E9 * 1.602E-19
1.84E-8 Coulombs
if a bunch passes a point every 25E-9 s
then in one second 4.0E7 bunches pass
the Amp is defined as 1 Coulomb per second passing a point
so you'd multiply the charge of a bunch of protons by the number of bunches passing per second
The definition of an electronVolt is the change in energy needed to change the particles potential by 1 Volt
for particles with a charge the size of the charge of one electron (like a proton) it's a straight 1:1 relationship between potential in V and energy in eV
6.5TeV protons have a potential of 6.5TV
--
one Volt is defined as one Joule per Coulomb
the size of the charge on an electron is
1.602E-19 Coloumbs
so one eV is equal to 1.602E-19 Joules
and you've got 115E9 particles with 6TeV energy each
--
the charge on a proton is 1.602E-19 Coulombs
so each bunch of 115E9 protons has a charge of 115E9 * 1.602E-19
1.84E-8 Coulombs
if a bunch passes a point every 25E-9 s
then in one second 4.0E7 bunches pass
the Amp is defined as 1 Coulomb per second passing a point
so you'd multiply the charge of a bunch of protons by the number of bunches passing per second
Is my working correct now? Please see my previous post 😊
Original post by LukeWatson4590
Thank you for your reply and further detailed explanation I truly appreciate it. I have tried to correct my solutions and have attached them below.
So for i. since 1 V = 1eV in a 1:1 relationship as you state;
6.5 TeV = 6.5 TV = 6.5 *10^12V?
ii. W=V * Q
Q=(115*10^9)*(1.602*10^-19)=1.8423*10^-8
W=(6.5 *10^12)*(1.84*10^-8)
W=119,749.5 J
iii. As you have shown in one second 4.0 ^ 10^7 bunches reach the collision point. The charge on a bunch of protons was earlier shown as 1.8423*10^-8 C.
So ( 4.0 ^ 10^7)*(1.8423*10^-8)=0.73692 A
Can I just check that I should multiply the charge of a bunch of protons by the number of bunches passing per second to find the average electric current, since surely this contradicts the formula I = Q/t ?
Thank you very much again 👍
So for i. since 1 V = 1eV in a 1:1 relationship as you state;
6.5 TeV = 6.5 TV = 6.5 *10^12V?
ii. W=V * Q
Q=(115*10^9)*(1.602*10^-19)=1.8423*10^-8
W=(6.5 *10^12)*(1.84*10^-8)
W=119,749.5 J
iii. As you have shown in one second 4.0 ^ 10^7 bunches reach the collision point. The charge on a bunch of protons was earlier shown as 1.8423*10^-8 C.
So ( 4.0 ^ 10^7)*(1.8423*10^-8)=0.73692 A
Can I just check that I should multiply the charge of a bunch of protons by the number of bunches passing per second to find the average electric current, since surely this contradicts the formula I = Q/t ?
Thank you very much again 👍
I'm not sure why you think that's not valid... amount of charge per second passing a point from
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
Original post by Joinedup
I'm not sure why you think that's not valid... amount of charge per second passing a point from
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
Thank you for your reply.
Sorry I am a bit confused can you demonstrate what you mean in your previous post?
Is my answer to iii wrong then? Since I have multiplied the charge of a bunch of protons by the number of bunches passing per second (=0.73692 ), is this equal to the number of protons per second?
Then by your statemnt do I need to multiply this by the charge per proton;
Charge per proton= 1.602*10^-19
So 0.73692 * (1.602*10^-19)=1.18*10^-19 A (is this the average electric current)?
I am sorry that I am struggling to understand this and honestly do greatly appreciate your help 😊
Original post by Joinedup
I'm not sure why you think that's not valid... amount of charge per second passing a point from
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
Sorry I am still a bit confused 😳 Please see my previous post 👍
(edited 4 years ago)
Original post by Joinedup
I'm not sure why you think that's not valid... amount of charge per second passing a point from
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
number of protons per bunch multiplied by number of bunches per second (to get you number of protons per second)
multiply that by charge per proton to get Q/t
Sorry I am still a bit confused 😳 Please see my previous post 👍
If you were in a sweet factory watching boxes of sweets go past on a conveyor belt and you were asked how many sweets went past in a certain abount of time AND you knew how many sweets were in each box.
all you'd have to do would be count the number of boxes passing your position in that time interval and multiply by the number of sweets in a box... that would give you the number of sweets passing in the time interval... right?
and if you knew the mass of each sweet you'd be able to multiply the mass of each sweet by the number of sweets you just calculated to get the total mass of sweets passing you in that time interval
all you'd have to do would be count the number of boxes passing your position in that time interval and multiply by the number of sweets in a box... that would give you the number of sweets passing in the time interval... right?
and if you knew the mass of each sweet you'd be able to multiply the mass of each sweet by the number of sweets you just calculated to get the total mass of sweets passing you in that time interval
Original post by Joinedup
If you were in a sweet factory watching boxes of sweets go past on a conveyor belt and you were asked how many sweets went past in a certain abount of time AND you knew how many sweets were in each box.
all you'd have to do would be count the number of boxes passing your position in that time interval and multiply by the number of sweets in a box... that would give you the number of sweets passing in the time interval... right?
and if you knew the mass of each sweet you'd be able to multiply the mass of each sweet by the number of sweets you just calculated to get the total mass of sweets passing you in that time interval
all you'd have to do would be count the number of boxes passing your position in that time interval and multiply by the number of sweets in a box... that would give you the number of sweets passing in the time interval... right?
and if you knew the mass of each sweet you'd be able to multiply the mass of each sweet by the number of sweets you just calculated to get the total mass of sweets passing you in that time interval
@Joinedup Great analogy thank you for your help. In this situation are you saying to find the total mass of the protons multiply the mass of one proton by the number of protons passing?
And are you also suggesting that the total number of protons per second is equal to the charge of a bunch of protons by the number of bunches passing per second ?
So would my answers as shown below now be correct?
i. 1 V = 1eV in a 1:1 relationship as you state;
6.5 TeV = 6.5 TV = 6.5 *10^12V?
ii. W=V * Q
Q=(115*10^9)*(1.602*10^-19)=1.8423*10^-8
W=(6.5 *10^12)*(1.84*10^-8)
W=119,749.5 J
iii. As you have shown in one second 4.0 ^ 10^7 bunches reach the collision point. The charge on a bunch of protons was earlier shown as 1.8423*10^-8 C.
So ( 4.0 ^ 10^7)*(1.8423*10^-8)=0.73692
0.73692 * (1.602*10^-19)=1.18*10^-19 A (average electric current)
😊👍
(edited 4 years ago)
Original post by Joinedup
If you were in a sweet factory watching boxes of sweets go past on a conveyor belt and you were asked how many sweets went past in a certain abount of time AND you knew how many sweets were in each box.
all you'd have to do would be count the number of boxes passing your position in that time interval and multiply by the number of sweets in a box... that would give you the number of sweets passing in the time interval... right?
and if you knew the mass of each sweet you'd be able to multiply the mass of each sweet by the number of sweets you just calculated to get the total mass of sweets passing you in that time interval
all you'd have to do would be count the number of boxes passing your position in that time interval and multiply by the number of sweets in a box... that would give you the number of sweets passing in the time interval... right?
and if you knew the mass of each sweet you'd be able to multiply the mass of each sweet by the number of sweets you just calculated to get the total mass of sweets passing you in that time interval
@JoinedupSo are my amended answers now correct? 😊👍
Sorry I am still confused 😳Have I arrived at a suitable solution?
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