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E=mc2 - mass energy conversion

Q1. The mass of the beryllium nucleus is 7.01473 u. What is the binding energy per nucleon of this nucleus?

Use the following data:

mass of proton = 1.00728 u

mass of neutron = 1.00867 u

mass defect = mass of nucleus - mass of individual nucleons

Δm = 7.01473u - (4 x 1.00728 + 3 x 1.00867)u = - 0.0404u

This is the mass that is changed becomes the 'binding energy'. That is the energy that would have to be put into the Berylium nucleus to pull it into its constituent nucleons. We use the conversion factor to change it into MeV equivalent.

EB = 0.0404 x 931.3 = 37.62

There are 7 nucleons so EB /nucleon = 37.62/7 = 5.37MeV

A
 1.6 MeV nucleon-1
B
 5.4 MeV nucleon-1
C
 9.4 MeV nucleon-1
D
 12.5 MeV nucleon-1

 

Q2. What is the mass difference of the nucleus ?

Use the following data:

mass of a proton = 1.00728 u

mass of a neutron = 1.00867 u

mass of a Li nucleus = 7.01436 u

mass defect = mass of nucleus - mass of individual nucleons

Δm = 7.01436u - (3 x 1.00728 + 4 x 1.00867)u = - 0.04216u

 

A
 0.03912 u
B
 0.04051 u
C
 0.04077 u
D
 0.04216 u

 

Q3. Uranium-236 undergoes nuclear fission to produce barium-144, krypton-89 and two free neutrons.

What is the energy released in this process?

Nuclide
Binding energy per nucleon / MeV
7.5
8.3
8.6

 

A
84 MeV
B
106 MeV
C
191 MeV
D
3730 MeV

 

+ +

Binding energy within the nuclei:

(236 x 7.5) (144 x 8.3) + (89 x 8.6) + zero (neutrons not bound) + energy freed

17701195.2 + 765.4 - 190.6

Energy freed = 191 MeV

Choice C