Atomic Mass Unit
The a.m.u. (Atomic mass unit) is very useful in nuclear physics.
Atomic mass unit is defined as \(\frac{1}{12}\)th of the mass of a \(6C^{12}\) atom.
According to Avogadro's hypothesis, the number of atoms in 12 gm of \(6C^{12}\) is equal to Avogadro's number i.e. \(6.023 \times 10^{23}\).
Hence, the mass of one carbon atom \((C^{12})\) is:
\[ \frac{12}{6.023 \times 10^{23}} = 1.992678 \times 10^{-26} \, \text{kg} \]
\(1 \, \text{a.m.u.} = \frac{1}{12} \times 1.992678 \times 10^{-26} = 1.660565 \times 10^{-27} \, \text{kg}\)
\[ 1 \, \text{a.m.u.} = 1.66 \times 10^{-27} \, \text{kg} \]
For examples:
- Mass of a proton \(m_p = 1.007275 \, \text{a.m.u.} = 1.672965 \times 10^{-27} \, \text{kg}\)
- Mass of a neutron \(m_n = 1.008665 \, \text{a.m.u.} = 1.67496 \times 10^{-27} \, \text{kg}\)
- Mass of hydrogen atom \(= 1.00794 \, \text{a.m.u.}\)
- Mass of chlorine atom \(= 35.47 \, \text{a.m.u.}\)