Question

Define nuclear force. Give its two most important characteristics.What is the energy released if all the deuterium atoms in a lake of cross sectional area 2.56 × 10⁵ (km)² and depth 80 m is used in fusion? Given abundance of ${}_{1}^{2}H = 0.0156 %$ of hydrogen density of water = 10³ kg m^-3 energy released due to fusion of one atom of ${}_{1}^{2}H = 7.17 MeV .$

Solution

Nuclear force is a strong attractive force acting between the nucleons of the atomic nucleus that holds the nucleus together.

Characteristics of nuclear force :

i) Nuclear forces are short range forces operating upto a distance which is of the order of a few fermi.

ii) Nuclear forces are strongest force in nature. It's magnitude is 100 times that of the electrostatic force and 10³⁸ times that of the gravitational force.

Numerical:

The volume V of lake is,

V = 2.56 \times 10^{5} \times 10^{6} \times 80 m^{3} = 2.048 \times 10^{13} m^{3}

∴

Mass of water, M in lake = 2.048 x 10¹³x 10³ = 2.048 x 10¹⁶kg
= 2.048 x 10¹⁹ gm

Now, 18 g of water contains 2 g of hydrogen.

∴

Mass of hydrogen atom in lake =

\frac{1}{9} \times 2.048 \times 10^{19} g

∴

Number of atoms of hydrogen in lake =

6.023 \times 10^{23} \times \frac{2.048 \times 10^{19}}{9}

= 1.37 \times 10^{42}

Since abundance of

{}_{1}^{2}H

is only 0.0156% of hydrogen atoms, the number of

{}_{1}^{2}H

atoms in lake,

= 1.37 \times 10^{42} \times 1.56 \times 10^{- 4} = 2.137 \times 10^{38}

Energy released due to fusion of one atom of

{}_{1}^{2}H = 7.17 MeV

∴

Energy released when all

{}_{1}^{2}H

atoms present undergo fusion,

= 2.137 \times 10^{38} \times 7.17 MeV = 1.532 \times 10^{39} MeV .

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