Define Atomic Mass Unit ? Show that Energy equivalent to 1 a.m.u is 931 MeV.

Define atomic mass unit. Express it in kg. Show that energy equivalent to 1 a.m.u. is 931 MeV.

Solutions: 

Atomic mass unit (amu or u) is defined as (1/12)th of the mass of a carbon-12 atom (i.e., ₆C¹²).

The mass of the nucleus and its constituent particles is expressed by a very small unit called unified mass unit (u). This unit is also known as atomic mass unit (a.m.u.), which is equal to 1.66 × 10⁻²⁷ kg 

According to Avogadro's hypothesis, 1 mole of a substance contains atoms equal to Avogadro's number:

N = 6.0225 × 10²³

Thus, 1 mole of carbon atoms contains 6.0225 × 10²³ atoms.

∴ Mass of 6.0225 × 10²³ carbon (₆C¹²) atoms = 12 g

or

Mass of 1 atom of carbon (₆C¹²)

= 12 / (6.0225 × 10²³) g

According to the definition of a.m.u.,

1 u or 1 a.m.u. = (1/12) × mass of 1 carbon atom (₆C¹²)

= $\frac{1}{12} \times \frac{12}{6.0225 \times 10^{23}}$

= 1.6604 × 10⁻²⁴ g

or

1 a.m.u. (i.e., 1 u) = 1.66 × 10⁻²⁷ kg

Mass of electron , $m_{e}= 0.00055 amu = 9.11 \times 10^{-31}kg$

Mass of proton , $m_{p} = 1.0073 amu = 1.6726 \times 10^{-27}$

Mass of proton , $m_{n} = 1.0086 amu = 1.6749 \times 10^{-27}$

Energy equivalent to 1 a.m.u. (or 1 u)

According to Einstein's mass-energy equation,

E = mc² ...(1)

Here,

m = 1 u = 1.66 × 10⁻²⁷ kg

c = speed of light in vacuum = 3 × 10⁸ m s⁻¹

∴ E = 1.66 × 10⁻²⁷ × (3 × 10⁸)²

E= 1.49 × 10⁻¹⁰ J

Since, 1 eV = 1.6 × 10⁻¹⁹ J

∴ $E = \frac{(1.49 \times 10^{-10})}{(1.6 \times 10^{-19})}$

E= 931.25 × 10⁶ eV

and

10⁶ eV = 1 MeV

∴ E = 931.25 MeV

Thus,

1 a.m.u. ≈ 931 MeV

Notes

1. Mass of a ₆C¹² (carbon atom) is nearly 1.993 × 10⁻²⁶ kg.

2. Atomic mass can be correctly measured with a mass spectrometer.

Frequently Asked Questions (FAQs)

1. What is Atomic Mass Unit (a.m.u.)?

Atomic Mass Unit (a.m.u. or u) is defined as one-twelfth (1/12) of the mass of a carbon-12 atom. Its value is 1.66 × 10⁻²⁷ kg.

2. What is the value of 1 a.m.u. in kilograms?

The value of 1 atomic mass unit is 1.66 × 10⁻²⁷ kg.

3. Show that the energy equivalent of 1 a.m.u. is 931 MeV.

Using Einstein's equation E = mc², where m = 1.66 × 10⁻²⁷ kg and c = 3 × 10⁸ m/s, the energy equivalent of 1 a.m.u. is approximately 931 MeV.

4. Why is a.m.u. used?

The masses of atoms and subatomic particles are extremely small, so a.m.u. provides a convenient unit for expressing atomic and nuclear masses.

Notes : CBSE Class 12 Physics Chapter 13 Nuclei - Param Himalaya 

1. composition of the nucleus of an atom
2. Atomic Mass Unit 
3. Proton: Definition, Discovery and Properties 
4. Neutron: Definition, Discovery and Properties
5. Define Isotopes, Isobars and Isotones with Example 
6. Size of the Nucleus: Derivation of Radius and Nuclear Density
7. Einstein Mass-energy relation
8. Mass Defect and Nuclear Binding Energy
9. Binding energy per nucleon and its variation with mass number
10. Nuclear Force 
11. Radioactivity 
12. Nuclear fission.
13. Nuclear fusion.