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30 November, 05:02

How much energy must be supplied to break a single 21Ne nucleus into separated protons and neutrons if the nucleus has a mass of 20.98846 amu?

What is the nuclear binding energy for 1 {/rm mol} of {/rm ^{21}Ne}?

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  1. 30 November, 07:36
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    1) There is 2.68 * 10^-11 J of energy needed

    2) The nuclear binding energy for 1 mol of Ne is 1.6 * 10^13 J/mol

    Explanation:

    Step 1: Data given

    The nucleus of a21Ne atom has a amass of 20.98846 amu.

    Step 2: Calculate number of protons and neutrons

    The number of electrons and protons in an 21Ne atom = 10

    The number of neutrons = 21 - 10 = 11

    Step 3: mass of the atom

    Mass of a proton = 1.00727647 u

    Mass of a neutron = 1.0086649 u

    The mass of the atom = mass of all neutrons + mass of protons

    Mass of atom = 11*1.0086649 + 10*1.00727647 = 21.1680786 amu

    Step 4: Calculate change of mass

    The change in mass = Mass of atom - mass of neon

    Δmass = 21.1680786 - 20.98846

    Δmass = 0.1796186

    Step 5: Calculate mass for a single nucleus

    The change of mass for a single nucleus is = Δmass / number of avogadro

    Δmass of nucleus = 0.1796186 / 6.022*10^23

    Δmass of nucleus = 2.98 * 10^-25 grams = 2.98 * 10^-28 kg

    Step 6: Calculate energy to break a Ne nucleus

    Calculate the amount of energy to break a Ne nucleus

    ΔEnucleus = Δmass of nucleus * c²

    ⇒ with c = 2.9979 * 10^8 m/s

    ΔEnucleus = 2.98 * 10^-28 kg * (2.9979*10^8) ² = 2.68 * 10^-11 J

    What is the nuclear binding energy for 1 mol of Ne?

    ΔE = ΔEnucleus * number of avogadro

    ΔE = 2.68 * 10^-11 J * 6.022*10^23

    ΔE = 1.6 * 10^13 J/mol
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