1 atomic mass unit is equal to

Question

Examoogle · Accepted Answer

Option A: $1.66 	imes 10^{-27} 	ext{ kg}$

Explanation & Concepts:
The atomic mass unit ($amu$ or $u$), also known as the unified atomic mass unit, is defined as exactly $\frac{1}{12}$ of the mass of an unbound neutral atom of carbon-12 at rest and in its ground state. Numerically, this constant is equivalent to $1.660539 	imes 10^{-27}$ kg.

Working Principle: The value is derived by dividing the molar mass of Carbon-12 ($12$ g/mol) by Avogadro's number ($N_A \approx 6.022 	imes 10^{23}$ atoms/mol) and then converting grams to kilograms. Since $1$ mole of Carbon-12 is $0.012$ kg, $1 u = \frac{0.012 	ext{ kg/mol}}{6.02214076 	imes 10^{23} 	ext{ mol}^{-1}} \approx 1.6605 	imes 10^{-27}$ kg.

Key Formulas: $1 u = \frac{M_{C-12}}{12 N_A} \approx 1.66 	imes 10^{-27} 	ext{ kg}$; $E = mc^2$ — used to equate mass difference in nuclei to energy in MeV

Key Points: It acts as a standard unit for measuring the mass of subatomic particles like protons and neutrons.; The mass of a proton is approximately $1.007 u$ and a neutron is $1.008 u$.; In nuclear physics, energy equivalents are often expressed as $1 u \approx 931.5$ MeV/$c^2$.

Advantages: Simplifies calculations of molecular and atomic masses.; Provides a consistent bridge between microscopic mass and macroscopic chemical units.

Applications: Nuclear binding energy calculations in power plants.; Mass spectrometry analysis.; Quantum chemistry and molecular dynamics.

Additional Info: The value $1.66 	imes 10^{-27}$ kg is standard for undergraduate physics.. Options B, C, and D provide powers of ten that are physically inconsistent with the mass of subatomic particles.

Answer: A is correct — The value of $1$ atomic mass unit is defined as $1.66 	imes 10^{-27}$ kg.

Exam Tip: Remember that $1 u$ is roughly the mass of one nucleon (proton or neutron); this helps quickly identify the order of magnitude in exam questions.

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Option B: $1.66 	imes 10^{-25} 	ext{ kg}$

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Option C: $1.66 	imes 10^{-17} 	ext{ kg}$

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Option D: $1.66 	imes 10^{-10} 	ext{ kg}$

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