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Under certain circumstances , a nucleus ...

Under certain circumstances , a nucleus can decay by emitting a particle more massive than an `alpha`-particle. Consider the following decay processes.
(a)`._88^223Ra to ._82^209Pb + ._6^14C`,
(b)`._88^223Ra to ._86^219 Rn + ._2^4He`
Calculate the Q-values for these two decays and determine that both are energetically possible.
`m(._88^223Ra) =223.01850 u, m(._82^209Pb)`=208.98107 u, `m(._86^219Rn)` = 219.00948 u, `m(._6^14C)` = 14.00324 u and `m(._2^4He)` =4.00260 u

Text Solution

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(a)`._88^223Ra to ._82^209Pb + ._6^14C +Q`
`therefore Q =[m_N(._88^223Ra)-m_N(._82^209Pb)-m_N(._6^14C)] xx 931.2 MeV`
`=[m._88^223 Ra - m(._82^209Pb ) - m (._6^14C) ] xx 931.2` MeV
=31.8 MeV
`because` O gt 0 , so, the decay is possible .
(b)`._88^223Ra to ._86^219Rn +._2^4He + Q'`
Q'=5.98 MeV [by similar calculation as above ]
`because` Q'=0 , so , this decay is also possible .
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