Calculate Kinetic Energy of 232Th to 228Ra/Alpha Particle

In summary: Ra nucleus = 0.0176 x 228 = 4.01 amua) Kinetic energy of 228 Ra nucleus = 6.54 x 10^-3 J - Kinetic energy of alpha particle = 6.54 x 10^-3 J - (4.01 amu x (299792458 m/s)^2) = 6.54 x 10^-3 J - (3.60 x 10^-12 J) = 6.54 x 10^-3 J - 3.60 x 10^-12 J = 6.53999996 x 10^-3 J
  • #1
MAPgirl23
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A 232 Th (thorium) nucleus at rest decays to a 228 Ra (radon) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 x 10^-3 J. An alpha particle has 1.76% of the mass of a 228 Ra nucleus.

a) Calculate the kinetic energy of the recoiling 228 Ra nucleus.

b) Calculate the kinetic energy of the alpha particle.
 
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  • #2
MAPgirl23 said:
A 232 Th (thorium) nucleus at rest decays to a 228 Ra (radon) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 x 10^-3 J. An alpha particle has 1.76% of the mass of a 228 Ra nucleus.

a) Calculate the kinetic energy of the recoiling 228 Ra nucleus.

b) Calculate the kinetic energy of the alpha particle.

Please note that we DO have a Homework help section AND a set of instructions in that section on what you must show when you are trying to work on a problem.

Zz.
 
  • #3
MAPgirl23 said:
A 232 Th (thorium) nucleus at rest decays to a 228 Ra (radon) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 x 10^-3 J. An alpha particle has 1.76% of the mass of a 228 Ra nucleus.

a) Calculate the kinetic energy of the recoiling 228 Ra nucleus.

b) Calculate the kinetic energy of the alpha particle.
What is the speed of the alpha particle? What is its mass? Using conservation of momentum, what is the recoil speed of the 228 Ra nucleus?

AM
 

FAQ: Calculate Kinetic Energy of 232Th to 228Ra/Alpha Particle

1. What is the formula for calculating kinetic energy?

The formula for calculating kinetic energy is KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

2. How do I determine the mass of the alpha particle in the calculation?

The mass of an alpha particle is approximately 4 atomic mass units (amu). This value can be found in a periodic table or other reference materials.

3. What units should be used for the mass and velocity in the kinetic energy formula?

The mass should be in kilograms (kg) and the velocity should be in meters per second (m/s). This will result in the kinetic energy being measured in joules (J).

4. How does the kinetic energy of the alpha particle change during the decay process from 232Th to 228Ra?

The kinetic energy of the alpha particle will decrease as it moves through the decay process. This is because the mass of the resulting nucleus (228Ra) is less than the mass of the original nucleus (232Th), and according to the conservation of energy, the difference in mass is converted into energy (in this case, kinetic energy).

5. Can the kinetic energy of the alpha particle be calculated if the velocity is unknown?

No, the kinetic energy cannot be calculated without knowing the velocity of the alpha particle. However, the velocity can be determined using other known values, such as the distance traveled or time taken for the decay process to occur.

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