Determine the speed of a 15 MeV helium atom.

Verified step by step guidance

1. Convert the given energy of the helium atom from MeV to joules. Use the conversion factor: 1 MeV = 1.602 × 10⁻¹³ J.
2. Relate the kinetic energy of the helium atom to its speed using the formula for kinetic energy: $K_E=\frac{1}{2}m{v}^2$, where $m$ is the mass of the helium atom and $v$ is its speed.
3. Determine the mass of the helium atom. Use the atomic mass of helium (approximately 4 u) and convert it to kilograms using the conversion factor: 1 u = 1.660 × 10⁻²⁷ kg.
4. Rearrange the kinetic energy formula to solve for the speed $v$: $v=\sqrt{\frac{2}{m}}$. Substitute the values for the kinetic energy (in joules) and the mass (in kilograms).
5. Perform the square root operation to find the speed of the helium atom. Ensure the units are consistent throughout the calculation to obtain the final speed in meters per second (m/s).

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is given by the formula KE = 1/2 mv², where m is the mass and v is the velocity of the object. In the context of particles, kinetic energy can also be expressed in electronvolts (eV), which is a unit of energy commonly used in particle physics.

Relativistic Effects

At high speeds, particularly those approaching the speed of light, relativistic effects become significant. According to Einstein's theory of relativity, the mass of an object increases with its speed, affecting its kinetic energy. For particles like helium atoms with high kinetic energy, the relativistic formula for kinetic energy must be used to accurately determine their speed.

Mass-Energy Equivalence

Mass-energy equivalence, expressed by the equation E=mc², indicates that mass can be converted into energy and vice versa. In particle physics, this principle is crucial for understanding how energy levels (like 15 MeV) relate to the mass of particles. When calculating the speed of a helium atom with a given energy, this concept helps in converting the energy into an equivalent mass to find the velocity.