Elastic collisions between proton and helium nucleus

In summary, in an elastic collision between a proton and a helium nucleus, the proton was scattered through a 45 degree angle. The proportion of its initial energy lost can be determined using the elastic formula E2/E0=4\gamma(sin(1/2*\gamma)^2/(\gamma+1)^2 and the recoil angle of the helium nucleus can be calculated using the equation tan\theta1=(sin\Psi))/((cos(\Psi)+\gamma), where phi is the scattering angle in the ZM frame and gamma is the mass ratio of the two particles.
  • #1
pentazoid
146
0

Homework Statement




In an elastic collision between a proton and a helium nucleus at rest, the proton was scattered through an angle of 45 degrees. What proportion of its initial energy did it lose? what was the recoil angle of the helium nucleus?

Homework Equations



tan[tex]\theta[/tex]1=(sin[tex]\Psi[/tex]))/((cos([tex]\Psi[/tex])+[tex]\gamma[/tex])

[tex]\theta[/tex]2=1/2(pi-[tex]\Psi[/tex])

tan[tex]\theta[/tex]=(([tex]\gamma[/tex])+1)/([tex]\gamma[/tex]-1)*cot(.5*[tex]\gamma[/tex])

E2/E0=4[tex]\gamma[/tex](sin(1/2*[tex]\gamma[/tex])^2/([tex]\gamma[/tex]+1)^2

phi is the scaterttering angle in the ZM frame and gamma=m2/m1, the mass ratio of the two particles. [tex]\theta[/tex]2 is the recoil angle and [tex]\theta[/tex]1 is the scatter angle.

The Attempt at a Solution



mhelium=4*mproton , therefore gamma=1/4
[tex]\theta[/tex]1=45 degrees

tan(45 degrees)=sin(phi)/(cos(phi)+.25)
1=sin(phi)/(cos(phi)+.25)==> cos(phi)+.25=sin (phi)

not sure how I can determine phi with sin(phi)-cos*(phi)=.25 ; I know I need phi to determine the recoil angle.

not sure how to determined how much initial energy was lost but I know it probably will have to apply this elastic formulae:

E2/E0=4[tex]\gamma[/tex](sin(1/2*[tex]\gamma[/tex])^2/([tex]\gamma[/tex]+1)^2

Does E0 represent the initial energy?
 
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  • #2
pentazoid said:
not sure how I can determine phi with sin(phi)-cos*(phi)=.25

Hi pentazoid! :smile:

(have a phi: φ :wink:)

Hint: sin(φ - 45º) = sinφcos45º - cosφsin45º :wink:
 

Related to Elastic collisions between proton and helium nucleus

1. What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the total energy before and after the collision remains the same.

2. How do you determine if a collision between a proton and helium nucleus is elastic?

To determine if a collision is elastic, you need to calculate the total kinetic energy of the system before and after the collision. If the total kinetic energy remains the same, then the collision is considered elastic.

3. What happens during an elastic collision between a proton and helium nucleus?

During an elastic collision between a proton and helium nucleus, both particles exchange energy and momentum, but the total kinetic energy of the system remains the same.

4. What are the factors that affect the outcome of an elastic collision between a proton and helium nucleus?

The outcome of an elastic collision between a proton and helium nucleus is affected by the masses and velocities of the particles involved. The angle of collision and the type of forces acting on the particles also play a role.

5. Why are elastic collisions between a proton and helium nucleus important in scientific research?

Elastic collisions between a proton and helium nucleus are important in scientific research because they can provide valuable information about the properties and behavior of these particles. They also help in understanding the fundamental principles of energy and momentum conservation.

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