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Find the minimum kinetic energy of an al...

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.

Text Solution

Verified by Experts

The correct Answer is:
A, D
Since, the masses are given in atomic mass units, it is easiest to proceed by finding the mass difference between reactants and products in the same units and then multiplying by `931.5 MeV//u`. Thus, we have
`Q=(14.00307u+4.00260u-1.00783u-16.99913u)` `(931.5(MeV)/(u))`
`=-1.20MeV`
Q-value is negative. It means reaction is endothermic.
So, the minimum kinetic energy of `alpha`-particle to initiate this reaction would be
`K_(min)=|Q|(m_alpha/m_N+1)=(1.20)(4.00260/14.00307+1)`
`=1.54 MeV`
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