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

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 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}

 
Answers (1)
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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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