fusion reaction rates

[physica]

I try and do my problems by myself as opposed to running to this forum but once again I have simply come across something that has me stumped. This will be the third time I've posted here this semester. Hopefully I'll get better by the end of the year otherwise final exams are going to be shaky.

 

I have been asked to calculate the rate of the reaction of deuteron fusing with a proton. My units don't seem to add up as I have a kg^-1 extra at the end. I also know that the rate is wrong because the next question asks to prove that the mean lifetime of deuteron in this reaction is one second. When I divid the number of deuterons by the rate of the reaction and it is way out from one second.

 

I believe that most of my calculation is correct. The main problem I think is with the first fraction of the rate equation as that is where the extra kg^-1 comes from. The question doesn't give the mass fraction so looking at the examples in the textbook don't give much help at all. I've attached my approach to solving this question. The values given in the question that have been inserted in the approach are:

T, n_p, n_d, s(E_0). I worked out E_G and A_r in previous questions. Those questions asked to prove that these are: [value given] so I know they're right.

 

Would be so grateful if someone could point me in the right direction. I have been stuck on this for the last 3 days. It's like staring at a brick wall, I can see nothing that I can move.

 

[imatfaal]

[knownothingstabinthedark]

 

A_r should be in dimensionless ratio rather than kilos? I presume that denominator is some form of Reduced Mass * Charge_p * Charge_d - it seems strange to have charge in dimensionless ratios and not mass. And it would radically change the size of your answer and remove an errant kg-1

 

[/knownothingstabinthedark]

[physica]

A_r is the reduced mass. I calculated it in a previous question. I know it's right because the question asked to prove that the reduced mass is... and gave a value. The reduced mass can be defined by Kg or by a fraction with U (meaning atomic units) next to it. I'll the the atomic units but still won't they have to be included in the answer?

[imatfaal]

But the Zp and Zd are charges (I think) and they don't seem to have units attached, this is what made me think of ratios rather than absolute ie you havent included the e for elementary charge either. The AMU is basically proton or neutron mass - so these are kinda ratios too; and of course ratios wouldnt show up in the dimensions in the answer

[imatfaal]

 

nb - posted on behalf of physica