A Van de Graall generator produces a beam of 2.00-MeV deuterons, which are heavy hydrogen nuclei

step 1 In the first part of this problem, we are also to calculate the distance between the deutrons. L

A Van de Graall generator produces a beam of 2.00-MeV...

A Van de Graall generator produces a beam of $2.00-\mathrm{MeV}$ deuterons, which are heavy hydrogen nuclei containing a proton and a neutron. (a) If the beam current is $10.0 \mu \mathrm{A}$ how far apart are the deuterons? (b) Is the electric force of repulsion among them a significant factor in beam stability? Explain.

Key Concepts

Particle Spacing Estimation

The average distance between particles in a beam can be estimated by considering the time interval between the arrivals of consecutive particles (derived from the particle flux) and the velocity of the particles. This concept links the microscopic dynamics of individual particles to the macroscopic properties of the beam, providing an estimate of inter-particle spacing.

Beam Current and Particle Flux

Beam current is a measure of the rate at which charged particles (in this case deuterons) pass a given point, defined as the total charge per unit time. By dividing the beam current by the charge of a single deuteron, one can obtain the number of deuterons that pass per second, which is fundamental for understanding particle density and spacing in the beam.

Kinetic Energy and Particle Velocity

Particles accelerated in devices like a Van de Graaff generator gain kinetic energy, which in turn determines their velocity. Using the relationship KE = ½ m v², one can find the speed of the deuterons from their kinetic energy. This velocity is essential for calculating how far apart the particles are, as it provides the rate at which they travel between successive particles.

Coulomb Force and Electrostatic Repulsion

Charged particles exert forces on each other through Coulomb's law, where like charges repel. Evaluating whether this repulsive electric force significantly affects beam stability requires comparing the magnitude of the Coulomb forces to other forces and effects (such as the momentum of the high-speed particles). This concept helps determine the role of mutual repulsion in the overall behavior of charged particle beams.

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