Question

Energy equivalent of 1 amu is 931 MeV. If true enter 1, else enter 0.

Answer 1

Hint: In general, we can convert amu into kg by following formula as below
\[1amu=1.66\times {{10}^{-27}}kg\]
- Now we can use the Einstein’s mass energy equivalence given by \[E=m{{c}^{2}}\] where c = velocity of light \[3\times {{10}^{8}}m/s\]

Complete Solution :
As we have \[1amu=1.66\times {{10}^{-27}}kg\]
According Einstein’s mass energy formula \[E=m{{c}^{2}}\]
We have \[m=1amu=1.66\times {{10}^{-27}}kg\]
$c=3\times {{10}^{8}}\,m/\sec $

- Hence we can write
\[\Rightarrow E=1.66\times {{10}^{-27}}\times {{\left( 3\times {{10}^{8}} \right)}^{2}}\]
\[\Rightarrow E=14.94\times {{10}^{-11}}Joule\]
\[\Rightarrow E=\dfrac{14.94\times {{10}^{-11}}}{1.66\times {{10}^{-19}}}eV\] Since \[1eV=1.6\times {{10}^{-19}}J\]
 We obtain \[E=931\times {{10}^{6}}eV\]
- In general for a factor of one million $({{10}^{6}})$ we use prefix mega(M). Hence we can write above value of E as \[E=931MeV\]
Hence we have proved that energy equivalent to 1 amu is \[931MeV\]
Therefore, the statement given in the ques is true, we’ll enter 1 in our answer

Note: 1. Mass energy equivalence is the principle that says mass has an equivalent amount of energy and vice – versa.
2. Mass energy equivalence states that mass is concentrated energy. Also according to the theory of special relativity, there is a tremendous amount of energy in mass. This energy is very difficult to release but can be released through matter antimatter annihilation.
4. The reason why nuclear reactions are said (and observed) to release so much more energy than chemical reactions are because of the changes in mass. For example: in a collision of an electron and a proton, the mass of both the particles is annihilated (or wiped out) but it creates energy in the form of photons.
6. The discovery of mass – energy equivalence was essential to the development of theories of atomic fission and fusion reaction.
7. Atomic mass unit, often abbreviated as ‘amu’ refers to a mass exactly equal to one – twelfth mass of carbon – 12 atoms.
8. For any given isotope, the sum of the number of protons and neutrons in the nucleus is called the mass number. This is because each proton and each neutron weigh one atomic mass unit (amu). By adding the no. of protons and neutrons and multiplying by 1 amu, we can calculate the mass of the atom.