1. An atom of 179 Ta has a mass of 178.945930 amu. Calculate the binding energy

Question

1. An atom of 179Ta has a mass of 178.945930 amu. Calculate the binding energy per MOLE in kJ. Use the values:

mass of 1H atom = 1.007825 amu
mass of a neutron = 1.008665 amu
c = 2.99792 x 108 m/s

2. An atom of 112In has a mass of 111.905536 amu. Calculate the mass defect (deficit) in amu/atom. Use the masses:

mass of 1H atom = 1.007825 amu
mass of a neutron = 1.008665 amu
1 amu = 931.5 MeV

3. An atom of 28Na has a mass of 27.97878 amu. Calculate the binding energy in MeV per atom. Use the masses:

mass of 1H atom = 1.007825 amu
mass of a neutron = 1.008665 amu
1 amu = 931.5 MeV

Explanation / Answer

1) Ta : Atomic number is 73.
atomic mass is 179(given)
Observed mass is 178.945930 amu

Number of electrons = number of protons = atomic number = 73

Number of neutrons = atomic mass- atomic number= 179-73= 106

Predicted mass= ( number of protons* mass of protons) + ( number of neutrons* mass of neutrons) + ( number of electrons * mass of electrons)
= (73*1.007825)+(106*1.008665)+(73*0.000549)
=180.529792 amu

Mass defect=predicted mass- observed mass.
= 180.529792- 178.945930
=1.583862 amu
=1.583862 *1.6608*10^(-27) kg
= 2.63047801*10^(-27) kg

Binding energy = mass defect * c^2
=2.63047801*10^(-27)*(2.99792*10^8)^2
= 2.63047801*10^(-27) * 8.987524326*(10^16)
=23.6414851*(10^-11) joules
=23.6414851*(10^-14) KJ

2) In : Atomic number is 49.
atomic mass is 112(given)
Observed mass is 111.905536 amu

Number of electrons = number of protons = atomic number = 49

Number of neutrons = atomic mass- atomic number= 112-49= 63

Predicted mass= ( number of protons* mass of protons) + ( number of neutrons* mass of neutrons) + ( number of electrons * mass of electrons)
= (49*1.007825)+(63*1.008665)+(49*0.000549)
=112.956221 amu

Mass defect=predicted mass- observed mass.
= 112.956221 - 111.905536
=1.050685 amu.

3) Na : Atomic number is 11.
atomic mass is 28(given)
Observed mass is 27.97878 amu

Number of electrons = number of protons = atomic number = 11

Number of neutrons = atomic mass- atomic number= 28-11= 17

Predicted mass= ( number of protons* mass of protons) + ( number of neutrons* mass of neutrons) + ( number of electrons * mass of electrons)
= (11*1.007825)+(17*1.008665)+(11*0.000549)
=28.239419 amu

Mass defect=predicted mass- observed mass.
= 28.239419- 27.97878
=0.260639 amu
=0.260639 *1.6608*10^(-27) kg
= 0.432869251*10^(-27) kg

Binding energy = mass defect * c^2
=0.432869251*10^(-27)*(2.99792*10^8)^2
= 0.432869251*10^(-27) * 8.987524326*(10^16)
=3.890422925*(10^-11) joules
=3.890422925*(10^-11) /1.602*(10^-13)
=2.42847873* (10^2) Mev

Mev= joule/ 1.602*(10^-13)

Note: * represents multiplication
/ represents division
(10^11) ten power 11.
(10^-12) ten power -12.
(10^2) ten square.
C^2 --> c square.
Mass is electron = 0.000549amu

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