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How much energy must a bomberding proton...

How much energy must a bomberding proton possess to cause the reaction `._(3)Li^(7) + ._(1)H^(1) rarr ._(4)Be^(7) + ._(0)n^(1)`
(Mass of `._(3)Li^(7)` atom is `7.01400`, mass of `._(1)m^(1)` atom is `1.0783` , mass of `._(4)Be^(7)` atom is `7.01693`)

Text Solution

Verified by Experts

Since the mass of an atom includes the masses of the atomic electrons, the appropriate number of electron masses must be subtrracted from the given values.
Reactants : Total mass `= (7.01600 - 3m_(e)) + (1.0783 - 1m_(e)) = 8.0943 - 4_(m_(e))`
Products : Total mass `= (7.01693 - 4m_(e)) + 1.0087 = 8.02563 - 4m_(e)`
This energy is supplie as kinetic energy of the bombarding proton. the incident proton must have more than this energy because the system must posses some kinetic energy even after the reaction, so that momentum is conserved with momentum conservation taken into account, the minimum kinetic energy that the incident particle must posses can be found with the formula .
where, `W = - [(8.02563 - 4m_(e)) - (8.0943 - 4m_(e))] 931.5 MeV = - 63.96 MeV`
`E_(th) = - (1+m/M)Q = - (1+1/7) (-63.96) = 73.1 MeV`
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