# Conservation of Energy and Momentum of Particles

• Fanman22
In summary, the conversation discusses the emission of an alpha particle from an initial moving atomic nucleus, resulting in a decrease in velocity. Using conservation of momentum and kinetic energy, equations are set up to determine the velocity of the alpha particle. However, it is discovered that only conservation of momentum is necessary to solve the problem, as the energy is not conserved due to the formation of a new nucleus after the emission.
Fanman22
An atomic nucleus initially moving at 500 m/s emits an alpha particle in the direction of its velocity, and the new nucleus slows to 480 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 226 u, what speed does the alpha particle have when it is emitted?

Well this is what I came up with so far:
m1=226 V1=500 V1'=?
m2=4 V2=? V2'=480

Use Conservation of Momentum and conservation of kinetic energy to get these equations, respectively:

226(500) + 4(V2) = 226(V1') + 4(480) and...

.5(226)(500)^2 + .5(4)(V2)^2 = .5(226)(V1')^2 + .5(4)(480)^2

Hopefully this is correct so far...now I know I'm supposed to do substitution next, but I'm having some algebra problems.

I got V2= -2.77e4 + 56.5(V1')
I'm not sure if this is correct I'm ashamed to say it, but I'm having a lot of trouble doing the algebra after I substitute it into the other equation.

Energy is not conserved. All you need is conservation of momentum. Realize that after the decay the old nucleus (226u) becomes two particles: the alpha particle (4u) and a new, smaller nucleus (222u).

Thanks, my brain just isn't working anymore. I spend about 45minutes trying to do a ridiculous substitution method. You guys are saviors.

## 1. What is conservation of energy and momentum?

The conservation of energy and momentum is a fundamental principle in physics that states that the total amount of energy and momentum in a closed system remains constant over time. In other words, energy and momentum cannot be created or destroyed, they can only be transferred or transformed.

## 2. How does conservation of energy and momentum apply to particles?

Particles, such as atoms, molecules, and subatomic particles, also follow the principle of conservation of energy and momentum. In a system of particles, the total energy and momentum before and after any interaction or movement must be equal.

## 3. What is the relationship between energy and momentum?

Energy and momentum are closely related, as they are both conserved quantities. In fact, momentum can be defined as the product of mass and velocity, while energy can be defined as the product of mass, velocity, and the square of the speed of light. This relationship is described by Einstein's famous equation, E = mc^2.

## 4. Are there any exceptions to the conservation of energy and momentum?

While the conservation of energy and momentum is a fundamental principle, there are certain situations where it may appear to not hold true. For example, in the quantum world, particles can seemingly appear and disappear without a clear conservation of energy and momentum. However, this is due to the uncertainty principle and does not violate the overall principle of conservation.

## 5. How is conservation of energy and momentum applied in real-world situations?

The principle of conservation of energy and momentum has many practical applications in everyday life. It is used in engineering to design efficient machines and in the study of collisions and interactions between objects. It is also a crucial concept in fields such as astrophysics and nuclear energy, where the conservation of energy and momentum governs the behavior of particles on a larger scale.

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