Intense physics question, mix of radioactive decay and electromagnetism

[skg94]

Homework Statement

A sample of thorium-226 is stored in a lead box. Thorium-226 undergoes alpha decay. The lead box has a small opening on the left side to allow a stream of alpha particles to escape.

In the sample a nucleus of thorium-226 is at rest when it undergoes alpha decay. The daughter nucleus produced, radium 222, has a mass of 3.67 * 10 ^-25 kg and moves to the right at 3.10 * 10^5 m/s immediately after the decay. The Thorium-226 nucleus, the radium 222 nucleus and the alpha particle form an isolated system.

To the left of the lead box are two parallel plates, one positively charged and the other negatively charged, that together produce a uniform electric field. The parallel plates are 2.00cm apart. The escaping alpha particles are stopped by the electric force just before they reach the positively charged plate. The complete apparatus is in a vacuum.

Determine the magnitude of the electric force acting on an alpha particle

ANSWER: 4.87*10^-11 N

Homework Equations

E= v/d
alpha decay theory
E=Fe/q
V= ΔE/q

The Attempt at a Solution

I started by doing the alpha decay equations even though its already done.

I was thinking of using V = ΔE/q to find V, then find E using v/d, then use E to find Fe. Then i realized the speed given is for radium, not the alpha particle, and doesn't mention any charge on radium or thorium. The mass is also for radium. Seeing parallel plates I am going to assume i am going to have to Use E=V/d at some point. But how do i find potential difference? What charge would i use, velocity, mass? Is there something I am not figuring out?

 

[CWatters]

I got the right answer by..

Applying conservation of momentum to work out velocity of alpha particle.

Then noting that the alpha decelerates from that velocity to zero in 0.02m.

Applying standard equations of motion and Newtons 2nd.

Not sure if it's technically the right approach but the numbers were ok.

 

[skg94]

Hm momentum of what tho? Momentum of thorium equals momentum of alpha particle and radium?

 

[CWatters]

Yes. I just assumed conservation of momentum.

Before decay..

M_T226*V_T226 = 0

After decay..

M_R22*V_R22 + M_alpha*V_alpha = 0

I googled the mass of an alpha to allow V_alpha to be calculated but perhaps the mass cancels later, I didn't check.

 

[SammyS]

Yes. I just assumed conservation of momentum.

Before decay..

M_T226*V_T226 = 0

After decay..

M_R22*V_R222 + M_alpha*V_alpha = 0

I googled the mass of an alpha to allow V_alpha to be calculated but perhaps the mass cancels later, I didn't check.

Mass of alpha particle ≈ 4 AMU.

Mass of Ra-222 nucleus ≈ 222 AMU.

\displaystyle \frac{m_\text{Ra-222}}{m_\text{Alpha}}\approx\frac{111}{2}=55.5