Kinetic Energy of uranium particles

[Manh]

Homework Statement

A uranium-238 atom can break up into athorium-234 atom and a particle called an alpha particle, α-4. The numbers indicate the inertias of the atoms and the alpha particle in atomic mass units (1 amu = 1.66 × 10^−27 kg). When an uranium atom initially at rest breaks up, the thorium atom is observed to recoil with an x component of velocity of -2.1 × 10^5 m/s.

Homework Equations

K = 1/2mv^2

The Attempt at a Solution

K = 1/2(1.66 x 10^27 kg)(-2.1 x 10^5 m/s)^2
K = 3.66 X 10^-17 J

 

[DEvens]

There seems to be something missing from your problem statement. What are you meant to be calculating? You seem to have left the question out of the problem statement.

 

[Manh]

There seems to be something missing from your problem statement. What are you meant to be calculating? You seem to have left the question out of the problem statement.

How much of the uranium atom's internal energy is released in the breakup?
Express your answer to three significant digits and include the appropriate units.

 

[Orodruin]

You cannot just compute the kinetic energy of the daughter nucleus (which, by the way, is significantly heavier than 1 u). Most of the energy will be carried by the alpha particle.

 

[Manh]

You cannot just compute the kinetic energy of the daughter nucleus (which, by the way, is significantly heavier than 1 u). Most of the energy will be carried by the alpha particle.

So, what am I supposed to do since I only know the formula of kinetic energy?

 

[Orodruin]

You are supposed to compute the total kinetic energy of both particles.

 

[Manh]

You are supposed to compute the total kinetic energy of both particles.

Can you guide me how to do that? I know that the total mass of the atom and particle is 1.66 × 10^−27 kg and velocity of the atom is -2.1 × 10^5 m/s. These given values may be plugged into an equation, right?

 

[Orodruin]

As I already told you, that is not the mass of the particle. It is one atomic mass unit. You know the masses of all particles, if you reread the problem statement you should be able to figure out what they are.

You need to compute the velocity of the alpha particle to know its energy. How can you relate it to what you know?

 

[DEvens]

Can you guide me how to do that? I know that the total mass of the atom and particle is 1.66 × 10^−27 kg and velocity of the atom is -2.1 × 10^5 m/s. These given values may be plugged into an equation, right?

You need to look at the mass of the alpha particle. The problem statement tells you it is $\alpha$-4. This is two protons and two neutrons. But look up the exact mass. Also look up the mass of a Thorium-234.

To get the energy of the Thorium nucleus, you need to conserve momentum. The alpha goes whizzing away in that direction. The Thorium goes the opposite direction. But the Uranium that started all this started at rest. So you conserve momentum. That tells you how fast the Thorium goes. Then you work out its kinetic energy.