In order to find the recoil velocity of a spring

[jgibbon2]

The nucleus of Po^214 decays radioactively by emitting an alpha particle (mass 6.65×10−27 kg) with kinetic energy 1.16×10−12 J, as measured in the laboratory reference frame.

a) Assuming that the Po was initially at rest in this frame, find the magnitude of the recoil velocity of the nucleus that remains after the decay.

in order to find the recoil velocity... i have tried v=-(sqrt KE*2m)/m ... is there a known mass for Polonium that you plug into this problem? where am i going wrong?

 

[Astronuc]

One must use conservation of energy and momentum.

The Po-214 nucleus has a mass of 214 amu (1 amu ~ 1.66 x 10^-27 kg)

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nucuni.html#c1

or use the mass of the alpha as 4 amu and that of the Po-214 nucleus as 214 amu.

 

[ogb p]

Your approach is correct, but you need to use the mass of the remaining nucleus, which is the mass of Po^210. This can be found by subtracting the mass of the alpha particle (6.65×10−27 kg) from the mass of Po^214 (2.14×10−25 kg). So, the mass of Po^210 is 2.14×10−25 kg - 6.65×10−27 kg = 2.0735×10−25 kg.

Using this mass, the recoil velocity can be calculated as:

v = -(√(2KE*m)/(m+M)) = -(√(2*1.16×10−12*6.65×10−27)/(6.65×10−27+2.0735×10−25)) = -1.39×10−6 m/s

This means that the nucleus of Po^210 will have a recoil velocity of 1.39×10−6 m/s in the opposite direction of the emitted alpha particle. It is important to note that this velocity is in the laboratory reference frame, so it may need to be converted to a different reference frame if necessary.