### E=mc 2 - Kalaheo High School

```Section 2: Mass Defect and E=mc2

Since an atom is made of protons, neutrons,
and electrons, you might expect the mass
of the atom to be the same as the mass of
all of these combined.
◦ However, this is not always the case. Lets look at He...
2 Protons: (2 x 1.007276 amu) = 2.014552 amu
2 Neutrons: (2 x 1.008665 amu) = 2.017330 amu
2 Electrons: (2 x 0.0005486 amu) = 0.001097 amu
Total combined = 4.032979 amu

The actual atomic mass of Helium
has been measured to be 4.002602
amu…
◦ The difference between the mass of an
atom and the sum of the masses of its
particles is called the mass defect.
◦ Sooooooooo where did the rest of the
mass go?!
 According to Einstein, it was converted directly
into energy! 

Albert Einstein developed an equation to
measure the amount of energy created when
the nucleus is created from loose particles
(fusion) or split apart (fission).
Energy
(Unit = J)
Δ Mass in Kg (mass of products– mass
of reactants)
2
E=mc
Constant
(3.00 x 108 m/s)
Speed of light in
a vacuum

Step 1: Calculate the mass of the reactants
and products…
◦
U+ n
Ba +
Kr + 2 n
◦ Mass of a neutron = 1.0087 amu
235
92
1
0
142
56
92
36
1
0
◦ Reactants: U (235) + n (1.0087) =
236.0087 amu
◦ Products: Ba (142) + Kr (92) + 2 n (1.0087
x 2) = 236.0174 amu
◦ Difference: 236.0174 – 236.0087 =
0.0087 amu

Step 2: Convert mass to Kilograms by
multiplying difference in mass (amu) by
1.6605 x 10-27 kg.
0.0087 amu x 1.6605 x 10-27 kg =
1.4447 x 10-29 kg
Now this number can be plugged into
the equation…

Step 3: Solve for E using mass (kg) and
constant (3.00 x 108 m/s)
E=mc2
E= (1.4447x10-29 kg)(3.00x108 m/s)2
E= (1.4447x10-29 kg) 9.00x1016 m2/s2
E= 1.30023 x 10-12 kg x m2/s2 = 1.30 x 10-12 J

Calculate the energy released when we split
U-235 into
235
92



U+
1
0
140
55
Cs and
n
140
55
92
37
Cs+
Rb.
92
37
Rb+ 2 n
1
0
235 + 1.0087 = 236.0087 amu (Reac)
140 + 92 + 2.0147 = 234.0174 amu (Prod)
Difference: 234.0174-236.0087=1.9913
amu x 1.6605x10-27 kg = 3.3066x10-27 kg
E=mc2
E= (3.3066x10-27 kg)(3.00x108 m/s)2
E= (3.3066x10-27 kg) 9.00x1016 m/s
E= 2.9754x10-10 kg x m2/s2 = 2.98 x 10-10 J
Uranium will release 2.98 x 10-10 J of
energy when it splits into Cs and Rb!

Calculate the energy released when two
Hydrogen isotopes fuse.
2
1




3
1
H+ H
4
2
He + n
1
0
2 + 3 = 5 amu (Reactants)
4 + 1.0087 = 5.0087 amu (Products)
Difference: 5.0087-5 = 0.0087 amu
Convert to Kg: 0.0087 amu x 1.6605x10-27
kg = 1.4447 x 10-29 kg
E=mc2
E= (1.4447x10-29 kg)(3.00x108 m/s)2
E= (1.4447x10-29 kg) 9.00x1016 m2/s2
E= 1.30023 x 10-12 kg x m2/s2 = 1.30 x 10-12 J
The two hydrogen isotopes will release
1.30 x 10-12 J of energy when they
fuse together!
```