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Binding Energy

Given the fol...

Question

Given the following binding energies:
1. $_{8}^{17} O \to 131 M e V$
2. $_{26}^{56} F e \to 493 M e V$
3. $_{92}^{238} U \to 1804 M e V$
Compare the binding energies per nucleon $(Δ = \frac{B}{A})$ of the three nuclei

A

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B

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C

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D

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Solution

The correct option is B
The binding energy per nucleon is just the average binding energy shared by each nucleon, given as,
$\frac{N e t b i n d i n g e n e r g y}{N u m b e r o f n u c l e o n s}$ = $\frac{N e t b i n d i n g e n e r g y B}{M a s s n u m b e r A}$
The upper left number, $i$ , in the representation $_{j}^{i} X$ tells us the mass number, or total number of nucleons in the nucleus. Therefore, for $_{8}^{17} O, A = 17. F o r_{26}^{56} F e, A = 56 . A n d f o r_{92}^{238} U, A = 238.$
${[\frac{B}{A}]}_{170} = \frac{131}{17} M e V = 7.7 M e V$
${[\frac{B}{A}]}_{56 F e} = \frac{493}{56} M e V = 8.8 M e V$
${[\frac{B}{A}]}_{238 U} = \frac{1804}{238} M e V = 7.6 M e V,$
Therefore, representing the binding energy by $D e l t a$
$Δ_{F e} > Δ_{0} > Δ_{U}$
Interesting, don't you think?
---------------------------------------------
P.S $∴$ To save a step, we could have calculated just $Δ_{0}$ and $Δ_{U}$ , since $Δ_{F e}$ is bound to be higher than both, being close to the top of the $D e l t a$ versus Agraph

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1._{8}^{17} O \to 131 M e V

2._{26}^{56} F e \to 493 M e V

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