Nuclear Reaction Threshold Energy Calculation

[hhhmortal]

Homework Statement

Hi, I'm trying to find out the formulae that gives me the threshold energy for a nuclear reaction (i.e. The minimum amount of energy required to induce a reaction).

I've got a question which states an endothermic reaction of :

O + p --> F + n has a Q value of -2.45 MeV.

Given that the atomic masses of O is 17.99916 u, neutron mass is 1.008665 u and proton mass is 1.007276 u, find the atomic mass of F.

I got this to be 18.00040

Second part says If the Oxygen (i.e. O) is at rest before the reaction, what is the threshold energy for the reaction.

I used :

[(-m_F + m_n)/m_F + m_n - m_p) ] Q = Threshold energy

Finally, third part says a proton is incident on an oxygen nucleus at rest, The neutron from the reaction is emitted at 90 to the incident beam. How can I calculate the energy of the incident proton?


Thanks very much.

 

[nickjer]

For the 2nd part you might want to clean up your equation a bit. I believe you mean:

$$E_{threshold} = -\frac{m_F+m_n}{m_F+m_n-m_p}Q$$

Also, for part 3 we aren't dealing with the threshold energy anymore. You should have an equation for minimum energy with respect to the angle. In the case of threshold energy, the angle of your products will be 0 degrees, since this makes the denominator maximum (giving you the absolute minimum energy).

In this case $\sin^2 (90) = 1$. Giving you the minimum denominator, and hence the largest energy with respect to angle.

Edit: Fixed the above equation.

 

[hhhmortal]

For the 2nd part you might want to clean up your equation a bit. I believe you mean:

$$E_{threshold} = -\frac{m_F+m_n}{m_F+m_n-m_p}$$

Also, for part 3 we aren't dealing with the threshold energy anymore. You should have an equation for minimum energy with respect to the angle. In the case of threshold energy, the angle of your products will be 0 degrees, since this makes the denominator maximum (giving you the absolute minimum energy).

In this case $\sin^2 (90) = 1$. Giving you the minimum denominator, and hence the largest energy with respect to angle.

Isn't the threshold energy equation multiplied by the Q value?

For the third part I have an equation which is quite long, but not sure if its the right one I should be using. The equation is going to be hard to post here seeing that I can't use LaTeX code, and I can't seem to find it online. Could you direct me to the relevant webpage with this equation please

Thanks.

 

[nickjer]

Click my equation and latex should appear. Try to mimic it. Also fixed my above equation.

 

[hhhmortal]

Ok then I gave it a go:


cos²θ = $$-\frac{m_F+m_n[m_FQ+(m_F-m_p)T_a]}{T_am_nm_p}$$

I inserted all the masses and set θ=90

And I found T_a to be 2.595 MeV

 

[nickjer]

I don't think that equation is right. The units don't come out right. You might want to double check it. Also, don't you have an equation for $T_a$ with $\theta$ in it.

 

[hhhmortal]

I don't think that equation is right. The units don't come out right. You might want to double check it. Also, don't you have an equation for $T_a$ with $\theta$ in it.

I found that equation in a book on nuclear physics (krane), and thought this was the one relevant to my question, but wasn't entirely certain. Not sure what you meant by an equation for $T_a$ with $\theta$, Isnt that what I already have?

 

[nickjer]

It would be best if you had it in the form $T_a(\theta)$ and not $\theta(T_a)$. Also, aren't you given this formula in the book where you got the homework problem from?

 

[hhhmortal]

It would be best if you had it in the form $T_a(\theta)$ and not $\theta(T_a)$. Also, aren't you given this formula in the book where you got the homework problem from?

Oh right! The problems were based on a book called Introductory nuclear physics ( Krane, Kenneth S), but are written by my lecturers.

 

[qweaszx]

can you solve problems 23-24-25-26-27 of chapter 11 for krane(introductory nuclear physics)??