Nuclear Fission and Nuclear Fusion

Nuclear Fission:

When a heavy nucleus breaks into two or more smaller, lighter nuclei and produces high energy, this process is called as nuclear fission.

Example:

$_{92}U^{235} +\: _{0}n^{1} (Neutron) \rightarrow \: _{92}U^{236} \rightarrow _{56}Ba^{141} + \: _{36}Kr^{92} + \: 3 _{0}n^{1} + \gamma$

Nuclear Fusion:

When two or more very light nuclei move with a very high speed then these nuclei are fused and form a single nucleus. This process is called as nuclear fusion.

Example: Two deuterons can be fused to form a triton(tritium nucleus) as shown in the reaction below:

$_{1}H^{2} + \: _{1}H^{2} \rightarrow \: _{1}H^{3} + \: _{1}H^{1} + \: 4.0 \: MeV \:(Energy)$

$_{1}H^{3} (Tritium) + _{1}H^{2} \rightarrow \: _{2}He^{4} + _{0}n^{1} + 17.6.0 \: MeV \:(Energy)$

The total result of the above two equations is the fusion of deuterons and produces an $\alpha - $ particle $(_{2}He^{4})$, a neutron $(_{0}n^{1})$ and a proton $(_{1}H^{1})$. The total released energy is $21.6 MeV$.

Alternatively, the fusion of three deutrons $(_{1}H^{2})$ into $\alpha -$ partice can takes place as follows:

$_{1}H^{2} + _{1}H^{2} \rightarrow \: _{2}He^{3} + _{0}n^{1} + 3.3 \: MeV \:(Energy)$

$_{2}He^{3} + _{1}H^{2} \rightarrow \: _{2}He^{4} + _{1}H^{1} + 18.3 \: MeV \:(Energy)$

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Mass Defect, Binding Energy and Binding Energy per nucleon

Binding Energy:

The difference between the total mass of individual nucleons (i.e. total number of proton and neutron) and actual mass of nucleus of that energy is called binding energy.

$\Delta m = \left (P \times m_{P} + N \times m_{N} \right) - m_{actual} \qquad (1)$

Where
$\Delta m \rightarrow$ Mass Defect
$P \rightarrow$ Number of Proton
$N \rightarrow$ Number of Neutron
$m_{actual} \rightarrow$ Actual mass of nucleus
$m_{P} \rightarrow$ Mass of a Proton
$m_{N} \rightarrow$ Mass of a Neutron

We know that

$Z=P=e \\ N=A-Z \qquad (2)$

Where
$Z \rightarrow $ Atomic Number
$A \rightarrow $ Atomic Mass Number
$ e \rightarrow $ Number of Electrons

From above two equation $(1)$ and equation $(2)$

$\Delta m = \left [ Z \times m_{P} + \left ( A-Z \right) \times m_{N} \right] - m_{actual} \qquad (1)$

Binding Energy:

The energy require to form or break a nucleous is called the binding energy of nucleous.

$B.E= \Delta m \times c^{2} Joule$

Where $B.E.\rightarrow$ Binding Energy

$B.E= \Delta m (in \: a.m.u.) \times 931.5 \: MeV$

Where $1 \: a.m.u. = 1.67377 \times 10^{-27} kilograms$

Binding energy per nucleon:

The energy require to emit one nucleon from the nucleous is called binding energy per nucleon.

$B.E. \: per \: nucleon = \frac{B.E.}{ Total \: No. \: of \: Nucleons}$

Where $B.E.\rightarrow$ Binding Energy

Note: Higher binding energy per nucleon shows higher stability of the nucleus.

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Spectrum of Hydrogen Atom

Description: The different series of hydrogen spectra can be explained by Bohr's theory. According to Bohr's theory, If the ionized state of a hydrogen atom be taken zero energy level, then energies of different energy levels of the atom can be expressed by following the formula

$E_{n}=\frac{Rhc}{n^{2}} \qquad (1)$

Where
$R \rightarrow$ Rydberg's Constant
$h \rightarrow$ Planck's Constant
$n \rightarrow$ Quantum Number

According to Plank's Theory

$E_{2} - E_{1} =h \nu \qquad(2)$

So from equation $(1)$

$E_{1}=\frac{Rhc}{n^{2}_{1}} $ and $E_{2}=\frac{Rhc}{n^{2}_{2}} \qquad (3)$

From equation $(2)$ and equation $(3)$

$\frac{Rhc}{n^{2}_{2}} - \frac{Rhc}{n^{2}_{1}} =h \nu $

$\frac{Rhc}{n^{2}_{2}} - \frac{Rhc}{n^{2}_{1}} = \frac{hc}{\lambda} $

$\frac{1}{\lambda}=R \left(\frac{1}{n^{2}_{1}} -\frac{1}{n^{2}_{2}} \right)$

The quantity $\frac{1}{\lambda}$ is called the 'wave number', All the series found in the hydrogen spectrum are explained by the above equation :

(i) Lyman Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 2, 3, 4, ...$) to the first energy level (lowest energy level), (i.e. $n_{1}= 1$), then spectral lines are emitted in the spectrum region of ultraviolet. The equation for obtaining the wavelengths of these spectral lines:

$\frac{1}{\lambda}=R \left(\frac{1}{1^{2}} -\frac{1}{n^{2}_{2}} \right)$

Where $n_{2} = 2, 3, 4, ...$

In 1916, Lyman photographed the lines of this series of hydrogen spectra. Hence, this series is named Lyman series'. The longest wavelength of this series (for $n_{2} = 2$) is $1216 A^{\circ}$ and the shortest wavelength (for $n_{2} = \infty$) is $912 A^{\circ}$. The wavelength $912 A^{\circ}$ corresponding to $n = \infty$ is called the 'series limit'.

(ii) Balmer Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 3, 4, 5, ...$) to the second energy level (i.e. $n_{1}= 2$), then the spectral lines are emitted in the spectrum region of the visible part.

$\frac{1}{\lambda}=R \left(\frac{1}{2^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2} = 3, 4, 5, ...$

In 1885, Balmer saw and studied first time these spectral lines. The longest wavelength of this series (for $n_{2} = 3$) is $6563 Å$ and the shortest wavelength (for $n_{2} = \infty$) is 3646 Ä.

(iii) Paschen Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 3, 4, 5, ...$) to the third energy level (i.e. $n_{1}= 3$) then the spectral lines are emitted in the spectrum region of infrared.

$\frac{1}{\lambda}=R \left(\frac{1}{3^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2} = 4, 5, 6, ...$

(iv) Brackett Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 5, 6, 7, ...$) to the fourth energy level (i.e. $n_{1}= 4$), then the spectral lines are also emitted in the spectrum region of infrared.

$\frac{1}{\lambda}=R \left(\frac{1}{4^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2} = 5,6, 7,.....$

(iv) Pfund Series: When an atom comes down from some higher energy level (i.e. $n_{2} = 6, 7, 8, ...$) to the fifth energy level (i.e. $n_{1}= 5$) then the spectral lines are also emitted in the spectrum region of infrared.

$\frac{1}{\lambda}=R \left(\frac{1}{5^{2}} -\frac{1}{n^{2}_{2}} \right)$

where $n_{2}= 6,7, 8, ....$

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Radioactive Decay and its types

Definition:

When the unstable atom (called radionuclide) loses its energy through ionizing radiation, this process is known as radioactive decay.

Types of radioactive decay:

There are 3- types of radioactive decay

1. Alpha Decay
2. Beta Decay
3. Gamma Decay

1. Alpha Decay: A helium nuclei which contain two protons and two neutrons is known as an alpha particle. The $\alpha$- particles are commonly emitted by the heavier radioactive nuclei. When the $\alpha$- particle is emitted from the nucleus then the atomic number is reduced by two (i.e. $Z-2$) or the atomic mass number is reduced by 4 (i.e. $A-4$).

Example:

The decay of $Pu^{239}$ into fissionable $U^{235}$ by the emission of $alpha$- particle

$_{94}Pu^{214} \rightarrow _{92}U^{235} + _{2}He^{4} \left(\alpha - particle \right)$

2. Beta Decay: The emission of $\beta$-particle occurs due to the conversion of a neutron into a proton or vice versa in the nucleus. The $\beta$-decay is commonly accompanied by the emission of neutrino ($\nu$) radiation. There are two types of $\beta$-decay.

i.) Beta Minus: When a neutron is converted into a proton then an electron ($_{-1}e^{\circ}$) i.e.$\beta$-minus particle is emitted. When the $\beta$- minus particle is emitted from the nucleus then the atomic number is increased by one (i.e. $Z+1$) and no change in atomic mass number ($A$).

Example:

$_{6}C^{14} \rightarrow _{7}N^{14} + _{-1}e^{\circ} + \overline{\nu}_{e} \: (anti\:neutrino)$

ii.) Beta Plus: When a proton is converted into a neutron then a positron ($_{+1}e^{\circ}$) $\beta$- plus partice is emitted. When the $\beta$- plus particle is emitted from the nucleus then the atomic number is decreased by one (i.e. $Z-1$) and no change in atomic mass number ($A$). It is also known as positron decay. Positron decay is caused when the radioactive nucleus contains an excess of protons.

Example:

$_{12}Mg^{23} \rightarrow _{11}Na^{23} + _{+1}e^{\circ} + \nu_{e}\: (neutrino)$

The penetrating power of $_{-1}\beta^{\circ}$ particles is small compared to $\gamma$-rays, however it is larger than that of $\alpha$-particles.

Note:

Electron Capture: The nucleus captures the electron from orbits and combines with a proton to form a neutron and emits a neutrino.

Example:

$_{26}Fe^{55} + _{-1}e^{\circ} \rightarrow _{25}Mn^{55} + \nu_{e}\: (neutrino)$

3. Gamma (y) Decay: $\gamma$-particles are electromagnetic radiation of extremely short wavelength and high frequency resulting in high energy. The $\gamma$-rays originate from the nucleus while X-rays come from the atom. $\gamma$-wavelength are on average, about one-tenth those of X-rays, though energy ranges overlap somewhat. There is no alternation of atomic or mass numbers due to $\gamma$ decay.

Example:

$_{27}Co^{60} \rightarrow _{27}Co^{60} + \gamma \: (gamma)$

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