NCERT · Class 12 · Physics · NucleiDefine atomic mass unit (amu) and calculate the energy equivalent of 1 amu in mega-electron volts (MeV).

Atomic mass unit (amu), or unified atomic mass unit (u), is defined as one-twelfth ($1/12^{\text{th}}$) of the mass of an unbound neutral carbon-12 atom in its nuclear and electronic ground state. Its standard value is approximately $1.660539 \times 10^{-27}$ kg. \nTo find the energy equivalent of 1 amu, we use Albert Einstein's mass-energy equivalence relation, $E = mc^2$. \nGiven data:

• Mass ($m$) = $1 \text{ amu} = 1.6605 \times 10^{-27} \text{ kg}$
• Speed of light ($c$) = $3 \times 10^8 \text{ m/s}$ \nStep 1: Calculate energy in Joules ($E$): $E = (1.6605 \times 10^{-27} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2$ $E = 1.6605 \times 10^{-27} \times 9 \times 10^{16}$ $E = 1.49445 \times 10^{-10} \text{ J}$ \nStep 2: Convert Joules into electron volts (eV) by dividing by the charge of an electron ($1.6 \times 10^{-19}$ C): $E = \frac{1.49445 \times 10^{-10}}{1.6 \times 10^{-19}} \text{ eV}$ $E = 9.34 \times 10^8 \text{ eV}$ \nStep 3: Convert eV into mega-electron volts (MeV) by dividing by $10^6$: $E \approx 931.5 \text{ MeV}$ \nThus, the energy equivalent of 1 amu is approximately 931.5 MeV.