The potential difference necessary to accelerate an He+ ion ?

In summary, to accelerate an He+ ion with a charge of +e and a mass of 4u from rest to a speed of 1.2×10^6 m/s, a potential difference of qV is needed, where q is the charge of the ion and V is the potential difference in volts.
  • #1
Netsurfer733
17
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The potential difference necessary to accelerate an He+ ion...?

Homework Statement



"What potential difference is needed to accelerate a He+ ion (charge +e, mass 4u) from rest to a speed of 1.2×10^6 m/s?"

Homework Equations



K_f + q*V_f = K_i + q*V_i

The Attempt at a Solution



I figure that:

q = 1.6*10^-19 for the charge of an electron I believe...?

I started off thinking these were somehow true:

V_f = (1/2) m*vf^2

V_i = (1/2) m*vi^2

but now I realize that's just silly, and they both equal K...which is the kinetic energy, sure...but I still have *no* idea what the V's are going to be!

I'm honestly kind of banging my head against the book here...it's not really teaching me what I need to do this problem in any reasonably understandable way. Can anyone help out with this?
 
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  • #2


What are the units of (electrical) potential difference? Volts, right? But the Volt is a "compound" unit comprising [Joules]/[Coulomb].

So a charge q accelerating though potential difference V will acquire kinetic energy qV:

ΔKE = q*ΔV
 
  • #3


You're absolutely right :D Got it, ty!
 

1. What is the potential difference necessary to accelerate an He+ ion?

The potential difference necessary to accelerate an He+ ion depends on several factors such as the mass and charge of the ion, the distance over which it needs to be accelerated, and the strength of the electric field. It can be calculated using the equation V = (q/m) * E * d, where V is the potential difference, q/m is the charge-to-mass ratio of the ion, E is the electric field strength, and d is the distance over which the ion needs to be accelerated.

2. How is the potential difference related to the acceleration of an He+ ion?

The potential difference is directly related to the acceleration of an He+ ion. This means that the higher the potential difference, the greater the acceleration of the ion. This is because the potential difference creates an electric field that exerts a force on the ion, accelerating it in the direction of the field.

3. Can the potential difference be too high for an He+ ion to accelerate?

Yes, the potential difference can be too high for an He+ ion to accelerate. If the potential difference is too high, it can cause the ion to gain too much energy and potentially break apart. This is known as overcharging and can have negative consequences in certain applications such as ion beam therapy.

4. Is there a minimum potential difference required to accelerate an He+ ion?

Yes, there is a minimum potential difference required to accelerate an He+ ion. This is because the ion needs to overcome its initial kinetic energy and the resistance of the electric field before it can start to accelerate. This minimum potential difference can be calculated using the equation V = (1/2) * (m/q) * (v^2), where m/q is the mass-to-charge ratio of the ion and v is its initial velocity.

5. How does the potential difference affect the speed of an He+ ion?

The potential difference has a direct impact on the speed of an He+ ion. The higher the potential difference, the greater the acceleration and therefore the higher the speed of the ion. However, once the ion reaches its maximum speed, increasing the potential difference will not result in a further increase in speed. This is because the ion has reached its maximum kinetic energy and cannot gain any more speed.

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