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The sun’s energy comes from nuclear reactions that fuse lighter nuclei into heavier ones, releasing energy in the process. The solar fusion process begins when two protons (the nuclei of hydrogen atoms) merge to produce a deuterium nucleus. Deuterium is the “heavy” isotope of hydrogen, with a nucleus consisting of a proton and a neutron. To become deuterium, one of the protons that fused has to turn into a neutron.  Our interest for now lies not with the nuclear physics but with the conditions that allow fusion to occur.                                                                            Before two protons can fuse, they must come into contact. However, the energy required to bring two protons into contact is considerable because the electric potential energy of the two protons increases rapidly as they approach each other. Fusion occurs in the core of the sun because the ultra-high temperature there gives the protons the kinetic energy they need to come together. a. A proton can be modeled as a charged sphere of diameterdp = 1.6 x 10-15 m with total charge e. When two protons are in contact, what is the electric potential of one proton at the center of the other?b. Two protons are approaching each other head-on, each with the same speed ν0. What value of ν0 is required for the protons to just come into contact with each other?c. What does the temperature of the sun’s core need to be so that the rms speed vrms of protons is equal to ν0?

The sun’s energy comes from nuclear reactions that fuse lighter nuclei into heavier ones, releasing energy in the process. The solar fusion process begins when two protons (the nuclei of hydrogen atoms) merge to produce a deuterium nucleus. Deuterium is the “heavy” isotope of hydrogen, with a nucleus consisting of a proton and a neutron. To become deuterium, one of the protons that fused has to turn into a neutron.  Our interest for now lies not with the nuclear physics but with the conditions that allow fusion to occur.                                                                            Before two protons can fuse, they must come into contact. However, the energy required to bring two protons into contact is considerable because the electric potential energy of the two protons increases rapidly as they approach each other. Fusion occurs in the core of the sun because the ultra-high temperature there gives the protons the kinetic energy they need to come together. a. A proton can be modeled as a charged sphere of diameterdp = 1.6 x 10-15 m with total charge e. When two protons are in contact, what is the electric potential of one proton at the center of the other?b. Two protons are approaching each other head-on, each with the same speed ν0. What value of ν0 is required for the protons to just come into contact with each other?c. What does the temperature of the sun’s core need to be so that the rms speed vrms of protons is equal to ν0?

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The sun’s energy comes from nuclear reactions that fuse lighter nuclei into heavier ones, releasing energy in the process. The solar fusion process begins when two protons (the nuclei of hydrogen atoms) merge to produce a deuterium nucleus. Deuterium is the “heavy” isotope of hydrogen, with a nucleus consisting of a proton and a neutron. To become deuterium, one of the protons that fused has to turn into a neutron.  Our interest for now lies not with the nuclear physics but with the conditions that allow fusion to occur.                                                                            Before two protons can fuse, they must come into contact. However, the energy required to bring two protons into contact is considerable because the electric potential energy of the two protons increases rapidly as they approach each other. Fusion occurs in the core of the sun because the ultra-high temperature there gives the protons the kinetic energy they need to come together.

a. A proton can be modeled as a charged sphere of diameter
dp = 1.6 x 10-15 m with total charge e. When two protons are in contact, what is the electric potential of one proton at the center of the other?
b. Two protons are approaching each other head-on, each with the same speed ν0. What value of ν0 is required for the protons to just come into contact with each other?
c. What does the temperature of the sun’s core need to be so that the rms speed vrms of protons is equal to ν0?

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