Find the minimum kinetic energy of an `alpha`-particle to cause the reaction `.^14N(alpha,p).^17O`. The masses of `.^14N`, `.^4He`, `.^1H` and `.^17O` are respectively `14.00307u`, `4.00260u, 1.00783u and 16.99913u`.

Explanation

`._(7)^(14)N+._(2)^(4)Herarr._(1)^(1)p+._(8)^(17)O`
`Q`-value of reaction
`[(4.00307 + 4.00260)-(1.00783+16.99913)]`
`=- 1.29 xx 10^(-3)u`
`=- 1.29 xx 10^(-3) xx 931.5 =- 1.2MeV`
`Q`-value is negative i.e reaction is endothermic.
Minimum kinetic energy of `alpha`-particle to initiate this reaction.
`K_(th) = K_(min) = |Q|((m_(alpha))/(m_(N))+1)`
`=(1.2)((4.00260)/(14.00307)+1)`
`= 1.54 MeV`