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 \times 10^{-27} \times (3 \times 10^{8})^{2}$

$E = 1.66  \times 10^{-27} \times 9 \times 10^{16}$

$E = 14.94 \times 10^{-17}$

$E = 1.494 \times 10^{-16}J$

Since, $1 eV = 1.6 \times  10^{-19}$ J

∴ $E = \frac{(1.49 \times 10^{-16})}{(1.6 \times 10^{-19})}$

$ E = 0.93125 \times 10^{-16} \times 10^{19}$

$ E = 931.24 \times 10^{3} \times 10^{-16+19}$

$ E = 931.24 \times 10^{3} \times 10^{3}$

$ E = 931.24 \times 10^{6} 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.