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10 December, 07:57

Calculate the nuclear binding energy for 5525mn in megaelectronvolts per nucleon (mev/nucleon).

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  1. 10 December, 08:05
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    To solve this question, let us first calculate how much all the nucleons will weigh when they are apart, that is:

    Mass of 25 protons = 25 (1.0073) = 25.1825 amu

    Mass of neutrons = (55-25) (1.0087) = 30.261 amu

    So, total mass of nucleons = 30.261+25.1825 = 55.4435 amu

    Now we subtract the mass of nucleons and mass of the Mn nucleus:

    55.4435 - 54.938 = 0.5055 amu

    This difference in mass is what we call as the mass defect of a nucleus. Now we calculate the binding energy using the formula:

    E=mc^2

    But first convert mass defect in units of SI (kg):

    Δm = 0.5055 amu = (0.5055) / (6.022x10^26)

    Δm = 8.3942x10^-28 kg

    Now applying the formula,

    E=Δm c^2

    E = (8.3942x10^-28) (3x10^8) ^2

    E=7.55x10^-11 J

    Convert energy from Joules to mev then divide by total number of nucleons (55):

    E = 7.55x10^-11 J * (6.242x10^12 mev / 1 J) / 55 nucleons

    E = 8.57 mev / nucleon
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