Question

In one fusion reaction that occurs in the cores of certain stars, a nucleus of helium-4 (4He, with two protons and two neutrons) fuses with a nucleus of neon-20 (20Ne, with 10 protons and 10 neutron) to form a nucleus of magnesium-24 (24Mg, with 12 protons and 12 neutrons). A gamma-ray photon (γ) is also produced:

4He + 20Ne → 24Mg + γ

(a) Rank the following nuclei in order of their binding energy per nucleon, from largest to smallest. If any two nuclei have the same binding energy per nucleon, state this. Explain how you made your ranking.

(i) The helium-4 (235U) nucleus

(ii) The neon-20 (134Te) nucleus

(iii) The magnesium-24 (99Zr) nucleus

(b) Using your results from part (a), explain why energy is released in the fusion of 4He and 20Ne.

(c) In the neutron-induced fission of uranium-235 (235U), the neutron that triggers the reaction can be moving very slowly relative to the 235U nucleus before they collide, with almost zero kinetic energy. But in order for the fusion of 4He and 20Ne to take place, the 4He nucleus must be moving very rapidly relative to the 20Ne nucleus before they collide. Explain why there is a difference.

Answer 1

I have solved your problem which is shown below:

Question :

(a) Rank the following nuclei in order of their binding energy per nucleon, from largest to smallest. If any two nuclei have the same binding energy per nucleon, state this. Explain how you made your ranking.

(i) The helium-4 (235U) nucleus

(ii) The neon-20 (134Te) nucleus

(iii) The magnesium-24 (99Zr) nucleus

Answer:

: Largest Binding energy per nucleon is of magnesium and then followed by Helium and then followed by Neon.

B.E per nucleon of Mg -24 = 8 MeV/c^2

B.E per nucleon of He-4 = 7.0725 MeV/c^2

B.E per nucleon of Neon -20 = 5.33 MeV/c^2

Because the ranking is based on the amount of energy gain by the nucleus during its decay chain rate. As when Uranium -235 decay alpha particle which is also known as He nucleus then the stability of daughter nuclei tells its binding energy. Similarly we can say about other nuclei’s.

Question:(b) Using your results from part (a), explain why energy is released in the fusion of 4He and 20Ne.

Answer: When He – 4 and Ne – 20 Combines to form a magnesium – 24 then large amount of energy is released because as we can see in part a the binding energy of Magnesium is more than helium and neon which corresponds to more the value of Binding energy per nucleon more energy is required to break nucleus into its constituents which leads to the formation of stable nucleus. As when helium and neon which has a Binding energy of 7.0725 and 5.33 MeV /c^2 but Magnesium has 8 MeV/c^2 which leads to higher stability of single nuclei and amount of energy released during the per nuclei or we can say per atom It will be (8 x 24) – ( (4x7.0725)+(20 x 5.33 )) = ( 192 ) - (28.29 + 106.6 ) = 57.11 MeV/c^2 Energy is released per reaction in the form of gamma photon.

Question (c) In the neutron-induced fission of uranium-235 (235U), the neutron that triggers the reaction can be moving very slowly relative to the 235U nucleus before they collide, with almost zero kinetic energy. But in order for the fusion of 4He and 20Ne to take place, the 4He nucleus must be moving very rapidly relative to the 20Ne nucleus before they collide. Explain why there is a difference.

Answer: In the neutron induced fission of uranium – 235 the neutron that triggers the reaction can be moving slowly relative to the U – 235 before the collide with almost zero kinetic energy because in the neutron induced fission the net charge on the neutron is neutral and it wont experience any electrostatic repulsion between the nuclei of uranium -235 and the neutron and it will trigger the nuclei reaction at very low Kinetic energy or it will have enough energy to start the chain reaction. Another reason is Uranium – 235 is unstable compound which requires only very small amount of energy to get into its excited state which leads to the chain reaction in uranium – 235. But in the nuclear fusion like in this case He – 4 and Ne – 20 the He has 2 protons and 2 Neutrons and Also Neon has 10 Protons and 10 Neutrons thus the 10 Protons inside the Neon will exert a Electrostatic Coloumb Repulsion on the atom of Helium which does not allow the He nuclei to enter the Neon nuclei and fusion process takes place. To overcome this Electrostatic repulsion between Helium and Neon we need to provide with efficient Kinetic energy so it will overcome this electrostatic repulsion and through quantum tunneling it will enter the neon the nucleus which leads to the formation of stable magnesium Nuclei and the Kinetic energy that is provided to the Helium atom is released in the form of gamma photon.

In case you have any query please write in a comment. I hope you like it. Thank you