Question

A uranium nucleus 238U may stay in one piece for billions of years, but sooner or later it decays into an α particle of mass 6.64×10−27 kg and 234Th nucleus of mass 3.88 × 10−25 kg, and the decay process itself is extremely fast (it takes about 10−20 s). Suppose the uranium nucleus was at rest just before the decay. If the α particle is emitted at a speed of 6.31×106 m/s, what would be the recoil speed of the thorium nucleus? Answer in units of m/s

Answer 1

Answer:

velocity of thorium will be $10.798\times 10^4m/sec$ ( in opposite direction )

Explanation:

We have given mass of alpha particle $m_{\alpha }=6.64\times 10^{-27}kg$

Speed of alpha particle $v_{\alpha }=6.31\times 10^{6}m/sec$

Mass of thorium $M_{TH}=3.88\times 10^{-25}kg$

We have to find the velocity of thorium

From conservation of momentum

$M_{\alpha }V_{\alpha }+M_{TH}V_{TH}=0$

$6.64\times 10^{-27}\times6.31\times 10^6+3.88\times 10^{-25}\times V_{TH}=0$

$V_{TH}=-10.798\times 10^4m/sec$

So velocity of thorium will be $10.798\times 10^4m/sec$ ( in opposite direction )