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Find Q-value and kinetic energy of the e...

Find Q-value and kinetic energy of the emitted `alpha`-particle in the `alpha`-decay of (a)`._88^222Ra` and (b)`._86^220Rn`. Given , `m(._86^226Ra)` = 226.02540 u, `m(._26^222Rn)` = 222.01750 u, `m(._86^220Rn)` = 220.01137 u, `m(._84^216Po)` = 216.00189 u , `m(._2^4He)` =4.00260 u

Text Solution

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(a)`._86^226Ra to ._86^222Rn + ._2^4He`
`therefore` Q-value =`m(._88^226Ra ) -[m(._86^222Rn)+ m(._2^4He)]`
=226.02540 - [222.0175 + 4.00260 ]
=0.0053 u = 0.0053 x 931.2 MeV
= 4.93 MeV
Kinetic energy of `alpha`-particle `=((A-4)/A) Q =(222-4)/222xx4.93`=4.84 MeV
(b)Similarly for `._86^220Rn` ,
Q-value = 6.41 MeV and kinetic energy of `alpha`-particle =6.29 MeV
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