Distance of Closest Approach of Proton & Alpha Particle

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In summary, the problem involves determining the distance of closest approach between a proton and an alpha particle, which both have initial speeds of 3.9×10^−3 c. The equation used to solve this problem was k(Q_p)(Q_a)/r=(.5(M_p)V^2)+(.5(M_a)V^2), and the correct answer is 1.3X10^-13m. The error in the attempt at solution may be due to not considering the frame of reference at the point of closest approach.
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seto6
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Homework Statement


An alpha particle is a nucleus of Helium. It has twice the charge and four times the mass of the proton.
A proton and an alpha particle headed directly toward each other, had each initial speed of 3.9×10^−3 c when they were far away.Here, as is customary when describing processes involving nuclear targets, the speed is expressed as a fraction of c, the speed of light.

What is the distance of closest approach between the proton and the alpha particle?

Homework Equations



potential energy and electric potential energy.

The Attempt at a Solution


following is a simplified attempt at solution

k(Q_p)(Q_a)/r=(.5(M_p)V^2)+(.5(M_a)V^2)
and solved for r and got 1.7X10^-13 m
but i keep getting it wrong could some 1 tell me where i am going wrong
the answer is 1.3X10^-13m
 
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  • #2
seto6 said:

Homework Statement


An alpha particle is a nucleus of Helium. It has twice the charge and four times the mass of the proton.
A proton and an alpha particle headed directly toward each other, had each initial speed of 3.9×10^−3 c when they were far away.Here, as is customary when describing processes involving nuclear targets, the speed is expressed as a fraction of c, the speed of light.

What is the distance of closest approach between the proton and the alpha particle?

Homework Equations



potential energy and electric potential energy.

The Attempt at a Solution


following is a simplified attempt at solution

k(Q_p)(Q_a)/r=(.5(M_p)V^2)+(.5(M_a)V^2)
and solved for r and got 1.7X10^-13 m
but i keep getting it wrong could some 1 tell me where i am going wrong
the answer is 1.3X10^-13m
The problem is the frame of reference you are using.

At the point of closest approach, are the two particles stopped in the lab frame? Why, or why not?

AM
 

1. What is the Distance of Closest Approach of Proton & Alpha Particle?

The distance of closest approach of a proton and an alpha particle is the shortest distance between the two particles during a collision or interaction. This distance is typically measured in units of nanometers (nm) or femtometers (fm).

2. How is the Distance of Closest Approach calculated?

The distance of closest approach is calculated using the Coulomb's Law, which states that the force between two charged particles is inversely proportional to the square of the distance between them. By equating the Coulomb force with the centripetal force, the distance of closest approach can be determined.

3. What factors affect the Distance of Closest Approach?

The distance of closest approach is primarily affected by the charges and masses of the interacting particles. As the charges increase, the distance of closest approach decreases. Similarly, as the masses increase, the distance of closest approach also increases. Other factors such as initial velocity and angle of collision may also affect the distance of closest approach.

4. Can the Distance of Closest Approach be changed?

Yes, the distance of closest approach can be changed by altering the initial conditions of the collision, such as the velocity, angle, or energy of the particles. Additionally, the use of external forces or fields, such as electric or magnetic fields, can also change the distance of closest approach.

5. What is the significance of the Distance of Closest Approach in nuclear reactions?

The distance of closest approach plays a crucial role in determining the outcome of nuclear reactions. If the distance of closest approach is small enough, the particles may undergo fusion or fission, releasing a significant amount of energy. However, if the distance of closest approach is large, the particles may simply scatter off each other without any significant interaction.

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