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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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ElectricalPower Generation
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1 atomic mass unit is equal to

A

1.66×10°−27 kg1.66 \times 10°{-27} \text{ kg}1.66×10°−27 kg

B

1.66×10°−25 kg1.66 \times 10°{-25} \text{ kg}1.66×10°−25 kg

C

1.66×10°−17 kg1.66 \times 10°{-17} \text{ kg}1.66×10°−17 kg

D

1.66×10°−10 kg1.66 \times 10°{-10} \text{ kg}1.66×10°−10 kg

Correct Answer

Concept & PrincipleElectricalPower Generation
Option A

1.66×10°−27 kg1.66 \times 10°{-27} \text{ kg}1.66×10°−27 kg

Quick Summary:

The atomic mass unit (amuamuamu or uuu), also known as the unified atomic mass unit, is defined as exactly 112\frac{1}{12}121​ of the mass of an unbound neutral atom of carbon-12 at rest and in its ground state. Numerically, this constant is equivalent to 1.660539×10°−271.660539 \times 10°{-27}1.660539×10°−27 kg.

💡 Explanation

The atomic mass unit (amuamuamu or uuu), also known as the unified atomic mass unit, is defined as exactly 112\frac{1}{12}121​ of the mass of an unbound neutral atom of carbon-12 at rest and in its ground state. Numerically, this constant is equivalent to 1.660539×10°−271.660539 \times 10°{-27}1.660539×10°−27 kg.

🔢 Key Formulas

1u=MC−1212NA≈1.66×10°−27 kg1 u = \frac{M_{C-12}}{12 N_A} \approx 1.66 \times 10°{-27} \text{ kg}1u=12NA​MC−12​​≈1.66×10°−27 kg

E=mc2E = mc^2E=mc2 — used to equate mass difference in nuclei to energy in MeV

⚙️ Working Principle

The value is derived by dividing the molar mass of Carbon-12 (121212 g/mol) by Avogadro's number (NA≈6.022×10°23N_A \approx 6.022 \times 10°{23}NA​≈6.022×10°23 atoms/mol) and then converting grams to kilograms. Since 111 mole of Carbon-12 is 0.0120.0120.012 kg, 1u=0.012 kg/mol6.02214076×10°23 mol−1≈1.6605×10°−271 u = \frac{0.012 \text{ kg/mol}}{6.02214076 \times 10°{23} \text{ mol}^{-1}} \approx 1.6605 \times 10°{-27}1u=6.02214076×10°23 mol−10.012 kg/mol​≈1.6605×10°−27 kg.

📌 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 1.007u1.007 u1.007u and a neutron is 1.008u1.008 u1.008u.

  • ▸

    In nuclear physics, energy equivalents are often expressed as 1u≈931.51 u \approx 931.51u≈931.5 MeV/c2c^2c2.

✅ Advantages
  • ▸

    Simplifies calculations of molecular and atomic masses.

  • ▸

    Provides a consistent bridge between microscopic mass and macroscopic chemical units.

🛠️ Applications / Uses
  • ▸

    Nuclear binding energy calculations in power plants.

  • ▸

    Mass spectrometry analysis.

  • ▸

    Quantum chemistry and molecular dynamics.

📄 Additional Information
  • ▸

    The value 1.66×10°−271.66 \times 10°{-27}1.66×10°−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.

✅

A is correct — The value of 111 atomic mass unit is defined as 1.66×10°−271.66 \times 10°{-27}1.66×10°−27 kg.

Core Concepts Used
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Atomic Mass Unit Avogadro's Constant Nuclear Physics Constants
💡 EXAM TIP

Remember that 1u1 u1u 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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