Consider the following a-decay of the Uranium nucleus 236 U 92 232 90 Th+a. (a) Show how the mass number (Aa) and atomic number (Za) of the alpha particle are obtained from this equation. (b) Calculate the Q-value (Qa) of the reaction. (c) Calculate the speed va = √2MQ of the alpha particle after it has been ejected from the parent mp nucleus, in terms of the speed of light c. M. mp and ma are the atomic masses = " (ma+mp) x ma of the daugher nucleus and the alpha particle, respectively.

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Consider the following a-decay of the Uranium nucleus
236 U → 332Th + a.
90
(a) Show how the mass number (Aa) and atomic number (Za) of the alpha particle are obtained from
this equation.
(b) Calculate the Q-value (Qa) of the reaction.
(c) Calculate the speed va = √2MQ of the alpha particle after it has been ejected from the parent
nucleus, in terms of the speed of light c. M =
-, mp and ma are the atomic masses
(ma+mp) x ma
mp
of the daugher nucleus and the alpha particle, respectively.
(d) Calculate the classical turning radius Re= 2Zpe²/Qa, where Zp is the atomic number of the
daughter nucleus, and e² = 1.44 MeV. fm.
(e) Calculate the decay probability Pa that the alpha particle will tunnel through the barrier.
HINT: In calculating the probability, use the fact that ħc=197.327 MeV fm. The formula to use
is given on page 5.
Transcribed Image Text:Consider the following a-decay of the Uranium nucleus 236 U → 332Th + a. 90 (a) Show how the mass number (Aa) and atomic number (Za) of the alpha particle are obtained from this equation. (b) Calculate the Q-value (Qa) of the reaction. (c) Calculate the speed va = √2MQ of the alpha particle after it has been ejected from the parent nucleus, in terms of the speed of light c. M = -, mp and ma are the atomic masses (ma+mp) x ma mp of the daugher nucleus and the alpha particle, respectively. (d) Calculate the classical turning radius Re= 2Zpe²/Qa, where Zp is the atomic number of the daughter nucleus, and e² = 1.44 MeV. fm. (e) Calculate the decay probability Pa that the alpha particle will tunnel through the barrier. HINT: In calculating the probability, use the fact that ħc=197.327 MeV fm. The formula to use is given on page 5.
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