Difference between revisions of "Solutions 4"

Revision as of 17:21, 18 June 2012

1:
Mass excess is given by deltaM(Z,A) = M(Z,A)-A. The masses can therefore be found with M(Z,A) = delta M (Z,A ) + A by using 1 u = 931.5 MeV we get:

• M(n) = 1.008665 u
• M(1H) = 1.007825 u
• M(4He) = 4.002603 u
• M(56Fe) = 55.934938 u
• M(142Ce) = 141.909244 u
• M(238U) = 238.050788 u

1. The most stable nuclei is ⁵⁶Fe. It has the highest binding energy compared to the number of nucleons.
2. 1.00 kg ²H is 496.5 mol by fusion 248,2 mol ⁴He is created which is 993.6 g. The difference in mass is equal to the energy 1000 g-993.6 g = 6.36 g. The energy is then 5.7 [math]\cdot[/math]10¹⁴ J, 3.56 [math]\cdot[/math] 10²⁷ MeV or 1.59 [math]\cdot[/math]10⁸ kWh.
3. 1.00 kg ²³³U fission to ⁹²Rb, ¹³⁸Cs and three neutrons. The mass difference is 0.785 g. Which gives 7,1[math]\cdot[/math]10¹³ J, 4.40 [math]\cdot[/math]10²⁶ MeV or 1.96[math]\cdot[/math]10⁷ kWh.
4. The energy from the fission is distributed in different ways: most of it goes to the kinetic energy of for the fission products. Other parts goes to the kinetic energy of the neutrinos and the neutrons, and some of it goes to “prompt” gamma-rays and beta/gamma rays from the fission products.

2:

binding energy B per nucleon:
[math]\frac{B}{A}=\frac{Z\cdot M(^{1}H)+N\cdot M(^{1}n)-M(A,Z)}{A}=[/math]

[math]\frac{12 \cdot 1.00782503207 + 12 \cdot 1.0086649156 - 23.985041}{24}=0.00868 \, u[/math]

It is 0.00868 u per nucleon

and 8.26 MeV per nucleon

3:

[math]\frac{E_{nucleus}}{E_{electron}}=\frac{8111.493 \, keV}{5.14\cdot 10^{-3} \, keV}=1.6\cdot 10^{5}[/math] times bigger binding energy for the nucleus.

4:

1. M(n) = 939.6 MeV.
2. M(e) = 0.511 MeV.
   
3. M("u") = 931.5 MeV.
   

5:

1. 8.55 MeV/nucleon.
   
2. 8.79 MeV/nucleon.
   
3. 7.86 MeV/nucleon.
   

6: The energy

M(²³⁵U) - (M(¹³¹Xe + M(¹⁰¹Ru) + 3M(n)) =

(ΔM(²³⁵U) + 235) - (Δ(¹³¹Xe) + 131) - (ΔM(¹⁰¹Ru) + 101) - 3(ΔM(m) + 1)

= ΔM(²³⁵U) - ΔM(¹³¹Xe) - ΔM(¹⁰¹Ru) - 3ΔM(n)

=40.916 + 88.421 + 87.952 - 3[math]\cdot[/math] 8.071 = 193.08 Mev

7:

Energy usage per 10 km:

1 L = 700 g. M_m(C₈H₁₈) = 114 g/mol, this means that 700 g is 6.14 mol.

6.14 mol [math]\cdot[/math]5500 kJ/mol = 33771.93 kJ, with a fuel efficiency of 18% the usage per 10 km is 6078.94 kJ/(10 km).

1 g ²³⁵U=4.25[math]\cdot[/math]10^-3 mol = 2.56[math]\cdot[/math]10²¹ atoms.

If all of the atoms fission and assuming 100% efficiency this will give 5.12[math]\cdot[/math]10²⁹ eV = 8.22[math]\cdot[/math]10⁷kJ. Which will last for 135190 km.

8:

ΔG = ΔG_{p'r'o'd'u'c't} - ΔG_{r'e'a'c't'a'n't} = - 237 k'J / m'o'l. Which means that for each H2O molecule it is generated 237kJ/NA = 2.456[math]\cdot[/math]10^-6MeV. Comparing to 0.0303 u = 23.2 MeV realesed by fusion to helium. We see that the nuclear reactions functions on a scale 10^6 times bigger than chemical.

9:

fusion of ²H gives 5.75[math]\cdot[/math]10¹¹ J/gram approximately ten times as much energy per fusion than uranium which gives 8.2[math]\cdot[/math]10¹⁰ J/gram

10:

In this problem it is usful to keep in mind the binding energy equation:

[math]B-{tot}(A,Z)=a_{v}A-a_{s}A^{2/3}-a_{c}\frac{Z^{2}}{A^{1/3}}-a_{a}\frac{A-2Z}{A}\pm\delta[/math]