Question

The half-lives of radioactive elements X and Y are 3 minute and 27 minutes respectively. If the activities of both are same, then the ratio of number of atoms of X and Y will be:
(A) 1:9
(B) 1:10
(C) 1:1
(D) 9:1

Answer 1

Hint We know that radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. Because the nucleus experiences the intense conflict between the two strongest forces in nature, it should not be surprising that there are many nuclear isotopes which are unstable and emit some kind of radiation. Instability of an atom's nucleus may result from an excess of either neutrons or protons. A radioactive atom will attempt to reach stability by ejecting nucleons (protons or neutrons), as well as other particles, or by releasing energy in other forms. An unstable nucleus spontaneously emits particles and energy in a process known as radioactive decay. The term radioactivity refers to the particles emitted. When enough particles and energy have been emitted to create a new, stable nucleus (often the nucleus of an entirely different element), radioactivity ceases.

Complete step by step answer
We know that the definition of elimination half-life is the length of time required for the concentration of a particular substance (typically a drug) to decrease to half of its starting dose in the body.
Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle. They need to be active long enough to treat the condition, but they should also have a short enough half-life so that they don't injure healthy cells and organs. The rate at which a radioactive isotope decays is measured in half-life. The term half-life is defined as the time it takes for one-half of the atoms of a radioactive material to disintegrate. Half-lives for various radioisotopes can range from a few microseconds to billions of years.
As, activity $\propto$ number of atoms $\times {\displaystyle \frac{1}{\text{ half }-\text{ life }}}\Rightarrow$ number of atoms $\propto$activity $\times$ half- life
So, the ratio of number of atoms of X and Y will be
$3:27=1:9$

Hence the correct option is option A.

Note It should be known that radioactive materials are hazardous. Nuclear radiation can ionise chemicals within a body, which changes the way the cells behave. It can also deposit large amounts of energy into the body, which can damage or destroy cells completely. Radiation can burn skin or cause cancer. Long-lived radioactive elements such as uranium, thorium and potassium and any of their decay products, such as radium and radon are examples of norm. These elements have always been present in the Earth's crust and atmosphere, and are concentrated in some places, such as uranium orebodies which may be mined.
We can say that nuclear reactions change in the identity or characteristics of an atomic nucleus, induced by bombarding it with an energetic particle. The bombarding particle may be an alpha particle, a gamma-ray photon, a neutron, a proton, or a heavy ion.