Minimum Initial Velocity for Deuterium Fusion in Center-of-Mass Frame

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SUMMARY

The minimum initial velocity required for two deuterium nuclei to overcome the Coulomb force and achieve fusion at a separation of 1 × 10-14 m is derived from the principles of electrostatics and kinetic energy. The relevant constants include the permittivity of free space (8.85419 × 10-12 C2/N·m2), the mass of a proton (1.67262 × 10-27 kg), and the mass of a neutron (1.67493 × 10-27 kg). The potential energy due to the Coulomb field must be calculated to determine the necessary kinetic energy for fusion, which directly relates to the initial velocity of the deuterium nuclei.

PREREQUISITES
  • Understanding of Coulomb's Law and electrostatic potential energy
  • Familiarity with the concept of center-of-mass frame in physics
  • Knowledge of basic nuclear physics, specifically deuterium properties
  • Ability to manipulate equations involving kinetic and potential energy
NEXT STEPS
  • Calculate the potential energy between two deuterium nuclei using Coulomb's Law
  • Determine the mass of a deuterium nucleus and its charge
  • Learn about the kinetic energy required for nuclear fusion reactions
  • Explore the concept of center-of-mass velocity in particle collisions
USEFUL FOR

Students and researchers in nuclear physics, particularly those studying fusion processes and the behavior of deuterium nuclei under electrostatic forces.

akmphy
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Please help me with this!

Two deuterium nuclei overcome the Coulomb
force of repulsion and attain the necessary
1 × 10−14 m distance for fusion.
What is the minimum initial velocity of
each nuclei, as measured in the center-of-
mass frame? The permittivity of free space
is 8.85419 × 10−12 C2/N · m2, the mass of a
proton is 1.67262 × 10−27 kg, the mass of a
neutron 1.67493 × 10−27 kg and the charge
on an electron −1.60218 × 10−19 C.
Answer in units of m/s.

2. Homework Equations
I do not know how to do this:
2mv.5(v)=ka/rm
r=separation b/w nuclei


3. The Attempt at a Solution
I am more than willing to work this out with someone. Usually I have an attempt; however, I believe I have no where to begin. Any help is appreciated.
 
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What's the mass of a deuterium nucleus? What's its charge?

What's the potential energy due to the Coulomb field for two deuterium nuclei at the specified separation?
 

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