How Do You Calculate the Recoil Speed of Thorium 234 After Particle Emission?

[mogley76]

Homework Statement

A Particle (x) of relative mass of 4 is emitted from a uranium 238 nucleus. Assuming the the particle (x) was originally at rest and was emitted with a speed of 1.4E7 m/s.
calculate the recoil speed of the residual nucleus (thorium 234)

Homework Equations

none given

The Attempt at a Solution

I know this is to do with the conservation of momentum. so P1=P2

p2=m2v2

so for particle (x) : (4*1.66E-27)*(1.4E7) = 9.296E-20 kgm/sbut initial velocity is 0 and i don't know how to go about calculating the recoil on the uranium nucleus? I am kinda lost..
can anyone help me out?

 

[tiny-tim]

hi mogley76!

first write out the general equation for conservation of momentum

 

[mogley76]

m1v1=m2v2 but v1 is 0 right? so I am kinda puzzled as to how i can workout the recoil speed..

 

[Fewmet]

m1v1=m2v2 but v1 is 0 right? so I am kinda puzzled as to how i can workout the recoil speed..

The momenta are equal in magnitude but opposite in direction, so that should be
m₁v₁ = -m₂v₂

You can also see this as
m₁v₁ + m₂v₂=0

Do you see how to go forward now?

 

[mogley76]

so...the recoil speed must be -1.4E7 m/s ? because thety both equal each other but in opposite directions?

 

[Fewmet]

so...the recoil speed must be -1.4E7 m/s ? because thety both equal each other but in opposite directions?

No: that would mean that the velocities are equal and opposite. The momenta are equal and opposite.

 

[tiny-tim]

hi mogley76!

(just got up :zzz: …)

m1v1=m2v2 but v1 is 0 right? so I am kinda puzzled as to how i can workout the recoil speed..

(try using the X₂ icon just above the Reply box )

you seem confused as to the basic equation …

conservation of momentum is ∑ mv before = ∑ mv after

in this case, "before" there is only one mass, and its speed is 0, so the LHS (∑ mv before) is 0

ie 0 = ∑ mv after