Calculating Alpha Particle Velocity from Initial Nucleus Motion

[Elvis]

CAN ANYONE HELP ME ?

An automatic nucleus initially moving at 500 m/s emits an alpha particle in the direction of its velocity, and the new nucleus shows to 450 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emmited ?

 

[berkeman]

Elvis, you must show your own work and attempt at a solution before we can help you with homework/coursework problems (see the "Rules" link at the top of the page).

What are the kinematic equations of motion that you will use to solve these problems? What energy balance equations can also be of help?

 

[Moetasim]

Hello,

I would be happy to assist you with your question. In order to calculate the velocity of the alpha particle when it is emitted, we can use the conservation of momentum principle. This principle states that the total momentum of a system remains constant unless acted upon by an external force.

In this case, we can assume that the system consists of the initial nucleus and the alpha particle. Before the emission, the total momentum of the system is given by:

P_initial = m_initial * v_initial

where m_initial is the mass of the initial nucleus and v_initial is its initial velocity.

After the emission, the total momentum of the system is given by:

P_final = m_final * v_final

where m_final is the mass of the new nucleus and v_final is its final velocity.

Since we know the initial and final velocities of the new nucleus, we can rewrite the equations as:

P_initial = (222 u) * (500 m/s) = 111000 u*m/s

P_final = (222 u + 4.0 u) * (450 m/s) = 100800 u*m/s

Since the total momentum of the system is conserved, we can equate these two equations and solve for the velocity of the alpha particle when it is emitted:

111000 u*m/s = 100800 u*m/s + m_alpha * v_alpha

where m_alpha is the mass of the alpha particle and v_alpha is its velocity.

Solving for v_alpha, we get:

v_alpha = (111000 u*m/s - 100800 u*m/s) / 4.0 u = 25100 m/s

Therefore, the velocity of the alpha particle when it is emitted is 25100 m/s.

I hope this helps to answer your question. Let me know if you have any further inquiries. Keep up the good work in your scientific studies!