Find the kinetic energy of the alpha particle

In summary: So, in summary, to determine the kinetic energy of the alpha particle in the rest frame of the Uranium-232 atom, we can use the equation KE_α = Q/(1+m_α/m_x), where Q is the energy released in the decay and m_α and m_x are the masses of the alpha particle and Thorium-228, respectively. This yields a value of approximately 5.4 MeV for the alpha particle's kinetic energy.
  • #1
Kyrios
28
0

Homework Statement



For the decay " Uranium-232 ---> Thorium-228 + alpha particle ",

What is the alpha particle's kinetic energy in the U-232 atom's rest frame?
We are given the masses for each one.

Homework Equations



E = mc^2

The Attempt at a Solution



I tried mass(U-232) - (mass(Th-228) + mass(α) ) = 5.9 x 10^ -3 u
And multiplied this by 931.5 to get E = 5.5 MeV.

Is this all there is to it? I was unsure what it meant by "in rest frame of U-232"
 
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  • #2
To conserve momentum, both Thorium and the alpha particle will move afterwards (in the rest frame of the initial nucleus). Therefore, Thorium will get some fraction of the released energy.
 
  • #3
Kyrios said:
I was unsure what it meant by "in rest frame of U-232"
It's conceivable, for example, that the uranium atom would be moving in the lab frame, and the question could have asked for the kinetic energy of the alpha particle that an observer at rest in the lab frame would see.
 
  • #4
mfb said:
To conserve momentum, both Thorium and the alpha particle will move afterwards (in the rest frame of the initial nucleus). Therefore, Thorium will get some fraction of the released energy.

I'm trying to work out the Kinetic energy of the alpha particle using this equation now:

[tex] KE_α = \frac{Q}{1+ \frac{m_α}{m_x}}[/tex]

Where Q is the energy I had before, the 5.5 MeV
m_α is the mass of the alpha particle and m_x is the thorium mass

I get a similar but slightly smaller answer, 5.4 MeV. Is that the right way of going about it?
 
  • #5
I don't know where the equation comes from, but it looks reasonable, and the result (slightly below 5.5 MeV) looks right.
 

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

How do you calculate kinetic energy?

Kinetic energy can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

What is an alpha particle?

An alpha particle is a type of particle that consists of two protons and two neutrons bound together. It is commonly emitted during radioactive decay.

How do you determine the kinetic energy of an alpha particle?

To determine the kinetic energy of an alpha particle, you will need to know its mass and velocity. Once you have these values, you can use the kinetic energy formula to calculate it.

Why is finding the kinetic energy of an alpha particle important?

Finding the kinetic energy of an alpha particle is important because it can help us understand the energy involved in radioactive processes, which have various applications in fields such as medicine and energy production. It can also provide insight into the behavior of particles at the atomic level.

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