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}?

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

it is to be noted that an alpha particle is an helium nucleus. so it contains 2 protons 2 neutrons and has a mass number of 4. when alpha decay particles are ejected from the nucleus it gets transformed into an atom which has atomic number less than 2 and a mass number less than 4.

an equation that could represent alpha decay is radium 226 decay of alpha particle forms radon 222.

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