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Question
Suppose, we think of fission of a `""_26^56"Fe"` nucleus into two equal fragments `""_13^28"Al"`. Is the fission energetically possible? Argue by working out Q of the process. Given `"m"(""_26^56 "Fe") = 55.93494 "u"` and `"m"(""_13^28 "Al") = 27.98191 "u"`.
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Solution
The fission of `""_26^56"Fe" ` can be given as:
\[\ce{^56_13 Fe -> 2 ^28_13 Al}\]
It is given that:
Atomic mass of `"m"(""_26^56 "Fe")` = 55.93494 u
Atomic mass of `m(""_13^28 "Al")` = 27.98191 u
The Q-value of this nuclear reaction is given as:
Q = `["m"(""_26^56 "Fe") - 2"m"(""_13^28 "Al")]"c"^2`
`= [55.93494 - 2 xx 27.98191]"c"^2`
`= (-0.02888 " c"^2) "u"`
But 1 u = 931.5 `"MeV/c"^2`
`therefore "Q" = - 0.02888 xx 931.5 = - 26.902` MeV
The Q-value of the fission is negative. Therefore, fission is not possible energetically. For an energetically-possible fission reaction, the Q-value must be positive.
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