Uranium 238 nucleus, initially at rest, emits an Alpha particle with the speed of 1.4*10^7 metre per second. Calculate the recoil speed of the residual nucleus Thorium 234 resume that mass of the nucleus is proportional to the mass number
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Solution
Mass∝Massnumber or mass=xA,where A is mass number
Thorium, mt=234x and mass of alpha particle, ma=4x
Velocity of alpha particle is va=1.4×107m/s and that of thorium is vt
Applying momentum conservation, mava+mtvt=0(rest)
so vt=−mavamt, after putting values of masses we get
vt=−2va117=−2.4×105m/s
Magnitude of velocity of residue nucleus i.e. Thorium nuclei is found to be 2.4×105m/s.