The mass of one \({}^{12}\mathrm{C}\) atom is \(1.992647\times10^{-26}\ \mathrm{kg}\). The atomic mass of \({}^{4}_{2}\mathrm{He}\) is 4.0026 u. The mass of one \({}^{4}_{2}\mathrm{He}\) atom is about
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(6.65\times10^{-27}\ \mathrm{kg}\)
One atomic mass unit is one-twelfth of the mass of a carbon-12 atom. First find 1 u in kilogram. Then multiply it by the atomic mass of helium.
\( \begin{aligned} 1\ \mathrm{u} &= \frac{\text{mass of one } {}^{12}\mathrm{C} \text{ atom}}{12} \\ &= \frac{1.992647\times10^{-26}}{12} \\ &= 1.6605\times10^{-27}\ \mathrm{kg} \end{aligned} \)
\( \begin{aligned} m_{\mathrm{He}} &= 4.0026\ \mathrm{u} \\ &= 4.0026\times1.6605\times10^{-27} \\ &= 6.65\times10^{-27}\ \mathrm{kg} \end{aligned} \)
NCERT (2026-27):
Atomic Masses and Composition of Nucleus – “… This unit is the atomic mass unit (u), defined as 1/12th of the mass of the carbon (12C) atom. According to this definition”
\( \displaystyle 1\mathrm{u}=\frac{\text{mass of one } {}^{12}\mathrm{C} \text{ atom}}{12}=\frac{1.992647\times10^{-26}\ \mathrm{kg}}{12}=1.660539\times10^{-27}\ \mathrm{kg} \qquad (13.1) \)