5.-/12.5 points ZinPhysLS35.P013 My Notes Ask Your Teacher Polonium-210 (210Po)

Question

5.-/12.5 points ZinPhysLS35.P013 My Notes Ask Your Teacher Polonium-210 (210Po) is a radioactive isotope that has an atomic nucleus with 84 protons and 126 neutrons (together, 210 nucleons). It undergoes an a-decay with a half-life of 138.4 days, resulting in a stable lead-206 (206Pb) isotope with a mass of 205.974 u. Assuming the polonium nucleus is at rest when it decays, an -particle (4He) with a speed of 1.6 × 107 m/s is emitted. The a-particle has a mass of 4.002 u. The atomic unit u is defined as 1-1.6605677 × 10-27 kg. (e) In what direction does the daughter isotope 206Pb move? In the opposite direction as the a-particle O In the same direction as the a-particle (b) What is the speed (in m/s) of the 206Pb leaving the decay zone? m/s (e) Compare both speeds in this problem to the speed of light in vacuum.

Explanation / Answer

a) In the opposite direction as the alfa-particle

b) Apply conservation of momentum

momentum of Pb = momentum of alfa particle in the opposite direction

m_Pb*v_pB = m_alfa*v_alfa

v_Pb = m_alfa*v_alfa/m_Pb

= 4*1.6*10^7/206

= 3.1*10^5 m/s

c) v_alfa/c = 1.6*10^7/(3*10^8) = 0.053

v_Pb/c = 3.1*10^5/(3*10^8) = 0.00103

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