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Atoms and Nuclei question

2007 · Shift 0 · Q63

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Atoms and Nuclei
2007 · Shift 0 · Q63

Atoms and Nuclei question

2007 · Shift 0 · Q63

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1

If

{M_O}

is the mass of an oxygen isotope

{}_8{O^{17}}

,

{M_p}

and

{M_N}

are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

A
$\left( {{M_O} - 17{M_N}} \right){C^2}$
B
$\left( {{M_O} - 8{M_P}} \right){C^2}$
C
$\left( {{M_O} - 8{M_P} - 9{M_N}} \right){C^2}$
D
${{M_O}{c^2}}$

View written solutionFree

Correct answer: $\BOXED{(8M_P + 9M_N - M_O)C^2}$

Identify the nucleus composition

For the isotope ${}_8O^{17}$ :

Atomic number $Z = 8$ $\Rightarrow$ number of protons $= 8$
Mass number $A = 17$ $\Rightarrow$ number of neutrons $= 17 - 8 = 9$

So the nucleus contains: $8\text{ protons and }9\text{ neutrons}$

Write the general expression for binding energy

Nuclear binding energy is given by: $B.E. = (\text{sum of masses of free nucleons} - \text{mass of nucleus})c^2$

Thus, $B.E. = \left(8M_p + 9M_N - M_O\right)c^2$

Compare with the given options

Option A: $\left(M_O - 17M_N\right)c^2$ This is incorrect because it does not include 8 protons separately.
Option B: $\left(M_O - 8M_p\right)c^2$ This ignores the 9 neutrons, so incorrect.
Option C: $\left(M_O - 8M_p - 9M_N\right)c^2$ This is the negative of the standard expression. The correct physical binding energy should be: $\left(8M_p + 9M_N - M_O\right)c^2$ So as written, this option has the wrong sign.
Option D: $M_Oc^2$ This is just rest energy of the isotope, not binding energy.

Conclusion

The correct expression for nuclear binding energy is: $\boxed{\left(8M_p + 9M_N - M_O\right)c^2}$

This does not match any option exactly. Option C has the correct masses involved but the sign is reversed.

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