Question

At a given instant, say t = 0, two radioactive substances a and b have equal activities. The ratio b a r r of their activities after time t itself decays with time t as e3t. [f the half-life of a is m2, the half-life of b is

Answer 1

some pieces of Uranium-Potassium-Sulphate with visible light. Next, he wrapped these pieces in black paper and separated it from a photographic plate by a piece of silver. He left it for several hours. When he developed the photographic plate, he found that there was blackening on the plate.

This meant that something was emitted by the compound which penetrated the silver and black paper and hit the plate. Subsequent experiments show that radioactivity is a nuclear phenomenon which occurs when an unstable nucleus undergoes a decay. This is called Radioactive Decay.

Radioactive Decay

There are three types of radioactive decays in nature:

α-decay –a helium nucleus (42He) is emitted

β-decay – where electrons or positrons (particles with the same mass as electrons, but with a charge exactly opposite to that of an electron) are emitted;

γ-decay – high energy (hundreds of keV or more) photons are emitted.



Law of Radioactive Decay

When a radioactive material undergoes α, β or γ-decay, the number of nuclei undergoing the decay, per unit time, is proportional to the total number of nuclei in the sample material. So,

If N = total number of nuclei in the sample and ΔN = number of nuclei that undergo decay in time Δt then,

ΔN/ Δt ∝ N

Or, ΔN/ Δt = λN … (1)

where λ = radioactive decay constant or disintegration constant. Now, the change in the number of nuclei in the sample is, dN = – ΔN in time Δt. Hence, the rate of change of N (in the limit Δt→ 0) is,

dN/dt = – λN

Or, dN/N = – λdt

Now, integrating both sides of the above equation,