Nuclear Forces and Nuclear Energy

NUCLEAR FORCES

The protons and neutrons are held together by the strong attractive forces inside the nucleus. These forces are called as nuclear forces.

(i) Nuclear forces are short-ranged. They exist in small region (of diameter 10^–15 m = 1 fm). The nuclear force between two nucleons decrease rapidly as the separation between them increases and becomes negligible at separation more than 10 fm.

(ii) Nuclear force are much stronger than electromagnetic force or gravitational attractive forces.

(iii) Nuclear force are independent of charge. The nuclear force between two proton is same as that between two neutrons or between a neutron and proton. This is known as charge independent character of nuclear forces.

In a typical nuclear reaction

(i) In nuclear reactions, sum of masses before reaction is greater than the sum of masses after the reaction. The difference in masses appears in form of energy following the Law of inter-conversion of mass & energy. The energy released in a nuclear reaction is called as Q Value of a reaction and is given as follows.

If difference in mass before and after the reaction is Dm amu

(Dm = mass of reactants minus mass of products)

then Q value = $\Delta$m (931) MeV

(ii) Law of conservation of momentum is also followed.

(iii) Total number of protons and neutrons should also remain same on both sides of a nuclear reaction.

Illustration 1: Calculate the Q-value of the nuclear reaction:

₀C¹² $\to$ ₁₀Ne²⁰ + ₂He⁴

The following data are given:

m(₆C¹²) = 12.000000 u

m(₁₀Ne²⁰) = 12.000000 u

m(₂Ne⁴) = 4.002603 u

Solution: The Q-value of this reaction may be easily calculated may be easily calculated from the masses of the individual nuclei.

Q = [2m (₆C¹²) – { m (₁₀Ne²⁰) + m (₂He⁴)}]e²

= 24.000000 – (19.992439 + 4.002603)} u x c²

= 4.618 MeV

NUCLEAR FISSION

The breaking of a heavy nucleus into two or more fragments of comparable masses, with the release of tremendous energy is called as nuclear fission. The most typical fission reaction occurs when slow moving neutrons strike ₉₂U²³⁵. The following nuclear reaction takes place.

${}_{92}{U}^{235}{+}_0{n}^1{\to }_{56}B{a}^{141}{+}_{36}K{r}^{92}+3{}_0{n}^1+200MeV$

If more than one of the neutrons produced in the above fission reaction are capable of inducing a fission reaction (provided U²³⁵ is available), then the number of fissions taking place at successive stages goes increasing at a very brisk rate and this generates a series of fissions. This is known as chain reaction. The chain reaction takes place only if the size of the fissionable material (U²³⁵) is greater than a certain size called the critical size.

If the number of fission in a given interval of time goes on increasing continuously, then a condition of explosion is created. In such cases, the chain reaction is known as uncontrolled chain reaction. This forms the basis of atomic bomb.

In a chain reaction, the fast moving neutrons are absorbed by certain substances known as moderators (like heavy water), then the number of fissions can be controlled and the chain reaction is such cases is known as controlled chain reaction. This forms the basis of a nuclear reactor.

Illustration 2: When a beta particle is emitted from a nucleus the effect on its neutron-proton ratio is

(A) increased (B) decreased

(C) remains same (D) first (1) then (2)

Solution: ${}_Z{X}^A\to {{}_{Z+}}_1{Y}^A+{}_{-1}{e}^0(\beta )+\bar{v}$

${}_0{n}^1\to {}_1{P}^1+{}_{-1}{e}^0(\beta )+\bar{v}\therefore \frac{N_n}{N_p}isdecreased$

NUCLEAR FUSION

The process in which two or more light nuclei are combined into a single nucleus with the release of tremendous amount of energy is called as nuclear fusion. Like a fission reaction, the sum of masses before the fusion (i.e. of light nuclei) is more than the sum of masses after the fusion (i.e. of bigger nucleus) and this difference appears as the fusion energy. The most typical fusion reaction is the fusion of two deuterium nuclei into helium.

${}_1{H}^1{+}_1{H}^2{\to }_{2}H{e}^4+21.6MeV$

For the fusion reaction to occur, the light nuclei are brought closer to each other (with a distance of 10^–14 m). This is possible only at very high temperature to counter the repulsive force between nuclei. Due to this reason, the fusion reaction is very difficult to perform. The inner core of sun is at very high temperature, and is suitable for fusion, in fact the source of sun's and other star's energy is the nuclear fusion reaction