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0. Math Review31m
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
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5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
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10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
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14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
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18. Waves & Sound3h 40m
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20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
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24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

25. Electric Potential

The ElectronVolt

Physics

25. Electric Potential

The ElectronVolt

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Problem 14b

Textbook Question

Determine the speed of a 15 MeV helium atom.

Verified step by step guidance

Convert the given energy of the helium atom from MeV to joules. Use the conversion factor: 1 MeV = 1.602 × 10⁻¹³ J.

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.

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.

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).

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).

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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 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.

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