(d) What is the kinetic energy of an electron traveling at velocity (c)?

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Identify the formula for kinetic energy: $KE = \frac{1}{2}mv^2$, where $m$ is the mass of the electron and $v$ is its velocity.

Determine the mass of an electron, which is approximately \$9.11 \times 10^{-31}$ kg.

Substitute the given velocity $v = c$ (the speed of light, approximately \$3.00 \times 10^8$ m/s) into the kinetic energy formula.

Calculate the expression $\frac{1}{2}mv^2$ using the known values for $m$ and $v$. Remember to square the velocity.

Ensure the units are consistent and check the calculation for any errors.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity of the object. In the context of particles like electrons, this concept is crucial for understanding how their speed affects their energy levels.

Relativistic Effects

When dealing with particles moving at speeds close to the speed of light (c), relativistic effects become significant. According to Einstein's theory of relativity, the classical kinetic energy formula is modified to account for the increase in mass and energy as an object's velocity approaches c, leading to the equation KE = (γ - 1)mc², where γ is the Lorentz factor.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², indicates that mass can be converted into energy and vice versa. For high-speed particles like electrons, this principle is essential for understanding how their kinetic energy relates to their mass and the energy they possess when traveling at relativistic speeds.