Curriculum
Radio Activity – It is the property by virtue of which a heavy element disintegrates itself without the help of any external agency. It is the phenomenon of spontaneous emission of radiation by heavy elements is called radioactivity.
Three Types of Radiations
| L-Rays | B-Rays | Y-Rays | |
| 1) | An l-particle has charge double the +ve charge of proton i.e. equal to Helium nucleus. | B-particles causes a -ve charge, equal to electron. | V-rays carries no charge. |
| 2) | Mass of an l-particles is roughly four times that of H-atom i.e. equal to the mass of Helium nucleus. | The mass of the B-particle is same as that of electron, equal to 9.1 10-31 kg. | They are the packets of high energy proton. The rest mass of a v-ray proton is zero. |
| 3) | The vel. of l-particles ranges between 1.4 107 m/s to 2.1 107 m/s | The velocity of B-particles ranges from 33% to 99% of the vel. of light | They travels with the velocity of light |
| 4) | L-particles are deflected by electric field as well as magnetic field. | They are also deflected by electric field as well as magnetic field. | Due to neutral particles, they are never deflected by electric field as well as magnetic field. |
| 5) | Because of large mass, the penetrating power of alpha-particles is very small. | Because of small mass, the penetrating power of beta-particle is large. | They have very large penetrating power as compared to alpha & beta rays. |
| 6) | They have large ionisation power due to large mass. | Their ionizing power is th that of an -particle | They have very small ionising power. |
| 7) | alpha-decay :- It is the phenomenon of emission of l-particle from a inadequate nucleus.
When a nucleus emits -particle, it’s mass no decreases by four (4) & charge no. decreases by (2). For example, when 92U238 undergoes L-decay, we have 90Th234 & the emission of L decay as :- 92U238 90Th234 + 2He4 as, in general ZXA Z-2YA-4 + 2He4 +theta |
beta-decay :- It is the phenomenon of emission of an electron from a radioactive nucleus.
When a nucleus emits -particle, mass no remains same & Atomic no. is increased by one. For example when 90Th234 & change no ‘91’. Thus, the reaction is :- 92U238 91Pa234 + -1e0 or, in general ZXA Z+1YA + -1e0 +theta |
gamma-decay :- It is the phenomenon of emission of v-ray photon from a radioactive nucleus.
Since photons do not have any charge as rest mass, therefore, in v-decay, daughter nucleus has the same charge no. & same mass no as those of parent nucleus. In general, the -decay can be represented as ZXA ZXA +gamma |
Half-life of a Radio-active element :- It is defined as the time during which half of the wo of the no. of atoms disintegrated at any time i.e N=No/z. It is denoted by T.
Hence, when t = T, N = No/2, eqn (3) becomes
\begin{equation}
\frac{N o}{2}=N o e^{-\lambda T} \Rightarrow \frac{1}{2}=e^{-\lambda T}=2=e^{\lambda T}
\end{equation}
on taking log on both sides, we have
\begin{equation}
\begin{array}{lll}
& \log x^2=\log e^{\lambda T} & {\left[l x^2=0.693\right]} \\
& =0.6931=\lambda T & \\
\text { or } & {\left[\mathrm{T}_{1 / 2}=\frac{0.6931}{\lambda}\right.} &
\end{array}
\end{equation} – (4)
Mean/Average Life of a Radioactive element :- It is defined as
\begin{equation}
\zeta=\frac{\text { Total life time of all the atoms }}{\text { Total no.of atoms }(\mathrm{No})}
\end{equation} – (1)
As we know that small no. of atoms (dN) decay in a small time at the life time of these atoms lies between t & (t+dt). If dt is taken very-very small, then age of each of the ‘dn’ atoms can be taken as t & total age of dN atoms – t.dN – (2)
For finding total life time of all the atoms, integrate eq (2) under the limit o to No as
\begin{equation}
\int_0^{N o .} t . d N
\end{equation} -(3)
Now, according to the definition of Average life, epn (1) may also be written as
\begin{equation}
\zeta=\int_0^{N o .} \frac{t \cdot d N}{N o}
\end{equation} -(4)
from decay law, we know that
\begin{equation}
\begin{aligned}
& \frac{d N}{d t}=\lambda \mathrm{N} \\
& \qquad \begin{array}{l}
\Rightarrow d N \cdot \lambda N d t \\
\text { Or } \quad d N=\lambda N o e^{-\lambda T} d t
\end{array}
\end{aligned}
\end{equation}
using the result in eqn (4), we have
\begin{equation}
\zeta=\int_0^{N o .} \frac{t\left(-\lambda N o e^{-\lambda t} d t\right)}{N o}=-\lambda \int_o^{N o} t e^{-\lambda t} d t
\end{equation} -(5)
Also, whew t = 0, N = No & When t = 8, N = o, the limit in the eqn (5) charger to
\begin{equation}
\zeta=-\lambda \int_o^{N o} t e^{-\lambda t} d t \quad \text { or } \quad \zeta=\Delta \int_o^8 t e^{-\lambda t} d t
\end{equation}
on integrating by parts, the above eqn becomes
\begin{equation}
\zeta=1 / \lambda
\end{equation} -(6)
Hence “average life of a radioactive element is reciprocal of the decay constant of the element.”
Relation between Half lift & Average life :- As we know that half-life of a radioactive element is
\begin{equation}
\begin{aligned}
&\mathrm{T}=\frac{0.6931}{\lambda} \quad \Rightarrow \quad \lambda=\frac{0.6931}{T}\\
&\text { But average the } \zeta=\frac{1}{\lambda}=\zeta=\frac{\mathrm{T}}{0.6931}=[\zeta=1.44 \mathrm{~T}]
\end{aligned}
\end{equation}
i.e average life is 1.44 times the half life of a radioactive element.
The term is also refused to the “activity of a substance”, denoted by either A or R.
\begin{equation}
\mathrm{As} \frac{\mathrm{dN}}{d t}=-\lambda \mathrm{N}=[\mathrm{R}=-\lambda \mathrm{N}]
\end{equation}
Units of Radioactivity :
a. curie (ci); 1 curve = 3.7 1010
b. Becquerel (Bq); 1Bq = i decays/sec.
c. Rutherford (Rd)] 1Rd = 106 decays/sec.