Question

A radium nucleus(Ra) at rest decays into a radon (Rn) nucleus and an alpha (a) particle.

m_Ra =56.5m_a

m_Rn =55.5m_a

a. Find the ratio of the speed V_a / V_Rn after the decay

b. Find the ratio of the magnitude of the momenta P_a / P_Rn after the decay

c. Find the ratio of kinetic energy KE_a / KE_Rn after the decay.

show work algebraically

Answer 1

conservation of momentum. Initially momentum of radium is zero.

After decay the radon and alpha particle move in opposite direction.

b)

$P_{a} = P_{Rn} ==> \frac{P_{a}}{P_{Rn}} = 1$

a)

$\frac{V_{a}}{V_{Rn}} = \frac{m_{Rn}}{m_{a}} = \frac{55.5 m_{a}}{m_{a}} = 55.5$

c)

$\frac{KE_{a}}{KE_{Rn}} = \frac{\frac{1}{2}m_{a}V_{a}^{2}}{\frac{1}{2}m_{Rn}V_{Rn}^{2}} = \left ( \frac{m_{a}}{m_{Rn}} \right )*\left ( \frac{V_{a}}{V_{Rn}} \right )^{2}= \left ( \frac{m_{a}}{55.5m_{a}} \right )*\left (55.5 \right )^{2}= 55.5$