How Do You Calculate the Energy of an Alpha Particle in an Ionization Chamber?

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To calculate the energy of an alpha particle in an ionization chamber, start by understanding that the current generated is due to the number of ion pairs created by the alpha particles. The energy required to create one ion pair is 30 eV, and the current (I) relates to the charge produced over time (Q/t). The number of alpha particles emitted per second can be determined from the source activity, and using the equation I = nNe, where n is the number of ion pairs per alpha particle and N is the number of alpha particles per second, allows for the calculation of energy. A common mistake is miscalculating the number of alpha particles emitted, which should be derived from the correct conversion of activity units. Once the number of ion pairs is established, the energy can be calculated using E = 30n.
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I'm having a problem on a homework problem that I have for one of my nuclear waste engineering courses. I'm not exactly sure where to start on it. I've been looking at different resources and I haven't found anything that I can use. The question is as follows:

Estimate the energy in MeV of an alpha particle from a source of activity 1.0 microcuries which creates a saturation current of 1.0*10^(-9) A in an inonisation chamber. Assume e = 1.6*10^(-19) C, 1 Ci = 3.7*10^(10) disintegrations per sec. and 30 eV is needed to produce on ion pair.

I'm not sure where to start on this problem, so if there are a few equations out there that someone could let me know about, I would be greatly appreciative.
 
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gump said:
Estimate the energy in MeV of an alpha particle from a source of activity 1.0 microcuries which creates a saturation current of 1.0*10^(-9) A in an inonisation chamber. Assume e = 1.6*10^(-19) C, 1 Ci = 3.7*10^(10) disintegrations per sec. and 30 eV is needed to produce on ion pair.

I'm not sure where to start on this problem, so if there are a few equations out there that someone could let me know about, I would be greatly appreciative.
I'll take a stab at it. The alpha particle shoots through a cloud of atoms and knocks electrons off a gas molecule. The issue is: how many does it knock off? If you knew that, you would know its energy (ie. n=E/30 eV).

The energy needed to ionise one molecule (creating an ion pair) is 30 eV. When this occurs you get a 'current' because the electrons move away from the +ions. The current, in this case, is the result of all the alpha particles being released from the source/second knocking off n electrons each. The current is the rate of charge flow. In this case, it is the number of ions (in coulombs - ie ne) produced per second.

If all of this is correct (and I am not guaranteeing it is, but it makes sense to me) what is the equation for n? where N is the number of alpha particles released from the source/second, n is the number of ion pairs created per alpha particle, e is the charge of one electron or ion in Coulombs, I =1.0E-9 Amperes. Once you find n then you can find E.

AM
 
okay... so this is where I'm at so far.

Since we know that the current is caused by the number of ion pairs generated per unit time, and I = Q/t, where Q = amount of charge (e = 1.6x10-19 C) and t = time, the time is 1.6x10-10 sec.

Using the equation (n(ion) /t) = (E(a)n(a) / 30 eV) where nion = number of electron pairs, t = time, E(a) = Energy of an alpha particle, and n(a) = number of alpha decays per second we can solve for E(a).

E(a) = 30 eV (1 ion pair) / n(a)(1.6x10-10 sec.)

Since we know that n(a) = a – nion where a = source strength, we get n(a) = (1.0x10-6 Ci – 3.7x1010 dis./sec.) = -3.7x1010 dis./sec.

This negative number is really confusing me, and I'm not sure where I'm going wrong. Do I have one of my equations messed up? or am I going wrong somewhere else?
 
gump said:
Since we know that the current is caused by the number of ion pairs generated per unit time, and I = Q/t, where Q = amount of charge (e = 1.6x10-19 C) and t = time, the time is 1.6x10-10 sec.
I don't follow you there. Why not use seconds?
Using the equation (n(ion) /t) = (E(a)n(a) / 30 eV) where nion = number of electron pairs, t = time, E(a) = Energy of an alpha particle, and n(a) = number of alpha decays per second we can solve for E(a).
Why not just state the equation for I and worry about E later? I get:
I = dQ/dt = nNe where n is number of ion pairs per alpha, N is the number of alpha particles per second and e is the current created per collision.

When you get n, you can find E = 30n.
Since we know that n(a) = a – nion where a = source strength, we get n(a) = (1.0x10-6 Ci – 3.7x1010 dis./sec.) = -3.7x1010 dis./sec.
I think you meant 1.0E-6 * 3.7E10 = 3.7E4 dis./sec. That is N (no. of alpha particles/sec).

With that you should have no difficulty finding n using n = I/Ne Then find E.

AM
 
Thanks for your help guys. It now makes sense. I really appreciate it.
 
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