Lon Thrusters NASA's Deep Space 1 and Dawn spacecraft...

lon Thrusters NASA's Deep Space 1 and Dawn spacecraft employed ion thrusters in which xenonions withacharge of $+1.60 \times 10^{-19} \mathrm{C}$ and a mass of $2.18 \times 10^{-25} \mathrm{kg}$ are accelerated through a potential difference of 1315 $\mathrm{V}$ . What is the speed of the xenon ions as they exit the thruster?

lon Thrusters NASA's Deep Space 1 and Dawn spacecraft employed ion thrusters in which xenonions withacharge of $+1.60 \times 10^{-19} \mathrm{C}$
and a mass of $2.18 \times 10^{-25} \mathrm{kg}$ are accelerated through a potential
difference of 1315 $\mathrm{V}$ . What is the speed of the xenon ions as they
exit the thruster?

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Key Concepts

Kinetic Energy and Velocity Calculation

The kinetic energy of a moving particle is given by one half of its mass times the velocity squared. By equating the kinetic energy to the energy gained from the electric field (charge times voltage), one can derive the formula to calculate the exit speed of the particle.

Ion Thrusters

Ion thrusters are a type of electric propulsion system that accelerates ions to high velocities using electric fields produced by a potential difference. This technology provides high exhaust velocity and efficient fuel usage, making it ideal for long-duration space missions.

Acceleration of Charged Particles

The acceleration of charged particles occurs when they experience a force from an electric field due to a potential difference. This process converts electrical energy into kinetic energy, enabling the particles to reach high speeds.

Energy Conversion in Electric Fields

In an electric field, the work done on a charged particle is the product of its charge and the potential difference through which it is accelerated. This energy is converted into kinetic energy, which can be calculated to determine the particle's velocity.

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