Q

# Solve this problem - Atoms And Nuclei - JEE Main-2

If $\dpi{100} M_{O}$  is the mass of an oxygen isotope $\dpi{100} _{8}O^{17},$ $\dpi{100} M_{p}\; and\; M_{N}$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

• Option 1)

$(M_{O}-17\, M_{N})c^{2}$

• Option 2)

$(M_{O}-8\, M_{p})c^{2}$

• Option 3)

$(M_{O}-8\, M_{p}-9\, M_{N})c^{2}$

• Option 4)

$M_{O}c^{2}$

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As we learnt in

Binding energy -

$B.E=\left [ Zm_{p}+(A-Z)m_{n}-M_{x} \right ]c^{2}$

amount of energy released when nucleons  come together to form a nuclei.

$M_{x}$ = mass of nuclei formed

- wherein

$m_{p}- mass\ of\ proton$

$m_{n}- mass\ of \ neutron$

$Z- atomic\ number$

$A- atomic\ mass$

Binding energy $=\left [ ZM_{p}+(A-Z) M_{N}-M\right ]c^{2}$

$=\left [ 8M_{p}+(17-8) M_{N}-M_{O}\right ]c^{2}$

$=(8M_{p}+9M_{N}-M_{O})c^{2}$

[But the option given is negative of this].

Correct option is 3.

Option 1)

$(M_{O}-17\, M_{N})c^{2}$

This is an incorrect option.

Option 2)

$(M_{O}-8\, M_{p})c^{2}$

This is an incorrect option.

Option 3)

$(M_{O}-8\, M_{p}-9\, M_{N})c^{2}$

This is the correct option.

Option 4)

$M_{O}c^{2}$

This is an incorrect option.

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