Energy Problem-what did I do wrong?

[quickclick330]

Energy Problem--what did I do wrong?

Fusion (or "thermonuclear") reactions take place inside a star such as our Sun. One fusion reaction results from a collision between a proton (1H) and a deuteron (2H, the nucleus of "heavy" hydrogen, consisting of a proton and a neutron). When these two nuclei touch, they undergo a nuclear reaction, forming a helium-3 (3He) nucleus (containing two protons and one neutron) and a high energy photon, called a gamma ray.

1H + 2H 3He +

One "unified atomic mass unit", denoted by the symbol "u", is equal to 1.66 10-27 kg. The rest mass of the proton is 1.0073 u, the rest mass of the deuteron is 2.0136 u, the rest mass of the helium-3 nucleus is 3.0155 u, and the gamma ray is massless.


so...

rest masses
proton = 1.0073 u
deuteron = 2.0136 u
helium-3 nucleus = 3.0155 u

What is the kinetic energy of the helium nucleus plus the energy of the photon in the final state? Because you will be calculating a small difference of large quantities, you will need to use 5 or more significant figures in this calculation.
KHe + E = joules


*I've aready found out that the equation is:

mprotonc^2 + mdeuteronc^2 +Ui = mheliumc^2 +Khelium + Egamma

*Eand earlier in the problem I got that the Ui between the proton and the deuteron is 1.152e-13 J


so to find out mc^2 for the proton, deuteron, and helium,

(for the proton)

= (1.0073u) *(1.66e-27 kg) *(3e8)^2 = 1.5049062 J

(for deteron)
= 3.0083184 J

(for helium)

= 4.505158 J


so you would sove for Khelium + Egamma and get

Khelium + Egamma = mprotonC^2 +mdeutronC^2 +Ui - mheliumc^2

and i get 9.5876e-13...which is wrong?

Where have I gone wrong? Any help is greatly appreciated! thanks!

 

[Nate810]

You have incorrectly calculated the value of mprotonc^2. The rest mass of the proton is 1.0073 u, not 1.0073 kg. This means your calculation should be (1.0073u) *(1.66e-27 kg) *(3e8)^2 = 2.42620e-13 J, instead of 1.5049062 J. Once you make this correction, your answer should be correct.

 

[m2003]

Hello, it seems like you have made a few errors in your calculations. First, when finding the rest mass of the proton, you used 1.0073u instead of 1.007276u. This small difference can lead to a significant error in your final result. Additionally, when finding the rest mass of the deuteron, you used 3.0083184 J instead of 3.0083884 J. This also contributes to the error in your final result.

Furthermore, when finding the kinetic energy of the helium nucleus, you should use the mass difference between the initial and final state, not the rest mass of the helium nucleus. This means that the equation should be:

Khelium + Egamma = mprotonc^2 + mdeutronc^2 + Ui - (mprotonc^2 + mdeutronc^2 + mheliumc^2)

= Ui - mheliumc^2

= 1.152e-13 J - (3.0155u * 1.66e-27 kg * (3e8)^2) = -5.099e-14 J

This result is negative because the energy is released in the form of a gamma ray, which has a negative energy value. Therefore, the total energy in the final state is:

Khelium + Egamma = -5.099e-14 J + (-1.152e-13 J) = -1.662e-13 J

I hope this helps you identify where you went wrong in your calculations. Remember to always double check your numbers and units to avoid errors. Keep up the good work in your scientific studies!