Volt and electronvolt

[Jacques]

I need to understand the relation between volt (V) and electronvolt (eV) in a system with particle and electric field.

Let say that we have 2 larges plates in a vacuum and two test charged particle a proton and an electron.

The distance between the plates is 1 meter. The electric potential between the plates is 100 volt and the charge of the particles are +1 and -1 elementary charge.

If the plate are large enought the electric field gradian is constant in the middle betwen the plate.

 

An electron at the negative plate will experience a force toward positive plate. I am tempted to tell that the electron will have an energy of 100 eV when it hit the positive plate. Is it right ???

Next if I do the inverse with the proton I am tempted to multiply with the proton_mass/electron_mass factor that give around 182,000 eV... That make no sense.??

The proton is 1820 more massive than the electron the magnitude of the charge is the same so the force exerted on them is the same but opposite direction. The electron being lighter will cross the gap a lot faster than the proton. The proton will accelerate less but for a longer time.

 

That where I am lost and cannot find an answer to the question : how do you calculate the voltage needed to bring a particle to a chosen energy ?:confused:

[swansont]

A particle with an elementary charge (e) will acquire an energy of 1 eV when accelerated through a potential difference of 1 Volt. E = qV

 

The proton will indeed move slower, but it has more mass. It will end up with the same energy.

[Jacques]

Thanks Swanson. That is what I expected, but was not sure. What was mixing up was the fact that the proton will undergo a smaller acceleration because of the mass, but for a much more long time. So the proton will move 1820 time slower than the electron ?

An alpha particle 1/4 the proton speed ?

An other question:

If I increase the voltage between the plate, is there a voltage where electron will get off the negative plate. I know the vacuum tube diode, where cathode is heated to emit electron. But without heating will it happen ?

If yes coating the cathode with a dielectric ceramic stop electron leaking from the cathode ?

[ecoli]

Thanks Swanson. That is what I expected, but was not sure. What was mixing up was the fact that the proton will undergo a smaller acceleration because of the mass, but for a much more long time. So the proton will move 1820 time slower than the electron ?

An alpha particle 1/4 the proton speed ?

It should move with a velocity according the relationship: KE = .5mv^2

 

An other question:

If I increase the voltage between the plate, is there a voltage where electron will get off the negative plate. I know the vacuum tube diode, where cathode is heated to emit electron. But without heating will it happen ?

If yes coating the cathode with a dielectric ceramic stop electron leaking from the cathode ?

I'm not entirely sure what this question is...

 

But I think it may be about the photoelectric effect? A voltage won't knock an electron off a metal. That can only happen when the applied energy is greater than the work function of the particular metal.

[swansont]

The speed ratios will be the square root of the mass ratios, since KE = 1/2 mv^2

 

Electron emission will occur without heating; this will depend on the voltage and the gap and is made worse by sharp corners or anything that isn't smooth. You've got an electric field, so you can get field emission (heating gives you electrons via thermionic emission). This was a problem with ion optics when I was doing my postdoc; we'd have elements with several kiloVolts of potential difference, and it would arc & spark before reaching the setpoint. The good news is that the spark tends to obliterate small protrusions, so the system would "condition" itself and not discharge after a while. The downside is that while you're doing this it gives off (soft) x-rays, depending on the voltage, which may cause problems.

 

A dielectric ceramic should improve this, as it will increase the capacitance and as an insulator you shouldn't get any leakage through the material.

[Jacques]

Ok Thanks all for your answers

[YT2095]

A particle with an elementary charge (e) will acquire an energy of 1 eV when accelerated through a potential difference of 1 Volt. E = qV

 

so for instance in an average color TV (CRT type) each electron will have a 26KeV charge when it hits the phosphor?

[swansont]

so for instance in an average color TV (CRT type) each electron will have a 26KeV charge when it hits the phosphor?

 

If it's a 26 kV set of plates, basically yes. There will possibly be some energy loss mechanisms, but if the electron goes where it was aimed, those should be very small.

[YT2095]

it was interesting when you mentioned about Protons being slower also, what happens in the case of Ions, say a Sodium ion or that of a heavier element such as Copper.

as induced in a Mass spectrometer.

 

is there a simple calculation that can be used to reckon it`s "speed" relative to say a single electron or a Proton per given charge?

 

maybe using it`s atomic mass, something like Sodium would be 22.99 times slower than a single proton?

[ecoli]

it was interesting when you mentioned about Protons being slower also, what happens in the case of Ions, say a Sodium ion or that of a heavier element such as Copper.

as induced in a Mass spectrometer.

 

is there a simple calculation that can be used to reckon it`s "speed" relative to say a single electron or a Proton per given charge?

 

maybe using it`s atomic mass, something like Sodium would be 22.99 times slower than a single proton?

Mass spects work by accelerating a particle, via a voltage across parallel plates and shooting it through a magnetic field.

 

Knowing the voltage and charge, you can solve for energy. Knowing the velocity and energy, you also measure the radius of its circular orbit in the magnetic field. Knowing that you can solve for the mass.

 

[math] E = qV ;

E=\frac{1}{2}mv^2 ;

F=\frac{mv^2}{r} = qvB[/math]

[swansont]

it was interesting when you mentioned about Protons being slower also, what happens in the case of Ions, say a Sodium ion or that of a heavier element such as Copper.

as induced in a Mass spectrometer.

 

is there a simple calculation that can be used to reckon it`s "speed" relative to say a single electron or a Proton per given charge?

 

maybe using it`s atomic mass, something like Sodium would be 22.99 times slower than a single proton?

 

Square root of the atomic mass number: Na will be 4.8 times slower than a proton. Assuming it's singly ionized.

[YT2095]

Nice answers, Thnx each

[Jacques]

I have something else bugging me.

The force felt by the charge particle is proportionnal to the charge of the particle and the charge of the plate:

[math]

\vec{F} = \frac{Q_1Q_2}{4\pi\varepsilon_0 r^2}

[/math]

The number of charges on the plate depend on the capacity of the two plates. If I cut the plates in half and apply the same voltage, there will be half the charge so the force should be half of what it was. But E=qV, the energy is the same. How come what wrong in my reasonning

Thanks

[insane_alien]

thats because the field between the plates is still more or less uniform. you can usually treat the plates as infinite.

[John Cuthber]

Not all mass specs use a magnetic field (at least in a conventional sense). Quadrupole systems use an alternating elctric field and a static one to sort ions by mass.

http://en.wikipedia.org/wiki/Quadrupole_mass_analyzer

More to the point, time of flight spectrometers produce a pulse of ions (typically from a laser pulse hitting the sample). They then acclerate these ions through a known field and wait for them to arrive at a detector. The heavier they are the less they get accelerated and so the longer they take. With a bit of maths you can calibrate that and get a mass spectrum.

http://en.wikipedia.org/wiki/Time-of-flight_mass_spectrometry