(II) What is the speed of an electron just before it hits a television screen after being accele

step 1 We know that kinetic energy k is equal to gamma minus 1 times mc square. And let's substitute ga

(II) What is the speed of an electron just before it hits a...

Key Concepts

Electric Potential Difference

This concept refers to the work done per unit charge in moving a charge between two points at different electrical potentials. In problems involving particle acceleration, an electron accelerated by a potential difference gains energy equal to the product of its charge and the voltage, which is fundamental to understanding how electrical energy is converted into kinetic energy.

Energy Conservation

Energy conservation is the principle that energy cannot be created or destroyed, only transformed from one form to another. In the context of electron acceleration, the electrical potential energy that the electron gains from the applied voltage is entirely converted into kinetic energy (neglecting losses), allowing one to equate the two and derive the electron’s speed.

Conversion of Electric Energy to Kinetic Energy

This concept explains that when an electron is accelerated through an electric potential difference, the work done on the electron (which is the product of the electron’s charge and the voltage) is converted into its kinetic energy. Understanding this conversion is essential for calculating the resulting speed of the electron.

Classical Kinetic Energy Formula

The classical kinetic energy formula, KE = ½mv², is used to relate the kinetic energy obtained by the electron to its speed. By setting the gained electrical potential energy equal to the electron’s kinetic energy, one can solve for the electron's speed. This approach is valid when the speeds involved are sufficiently less than the speed of light.

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