How to solve half-life problems?

Hint: The radioactive substances have unstable nuclei. As a result, the radioactive substances disintegrate and this leads to the formation of a stable nuclei and there is also release of some energy.

Complete step by step answer:
When the radioactive substance disintegrates to form a stable nucleus, there are three types of decays which take place, the alpha decay gives alpha particles and the beta decay forms a beta particle and the gamma decays forms a gamma particle. The material which has unstable nuclei is known as radioactive substance.
- The half life of an element is the time required for the sample to go under radioactive decay. The expression is mentioned below:
\[A(t)={{A}_{o}}\times {{(\dfrac{1}{2})}^{\dfrac{t}{{{t}_{\dfrac{1}{2}}}}}}\]
Where,
A(t) = the amount left after t years
${{A}_{0}}$ = initial amount of substance which undergoes decay
${{t}_{\dfrac{1}{2}}}$ = half life of the substance

Additional Information :
Let’s understand the three decays in detail:
The first decay is alpha decay. During this decay there is release of alpha particles from the nucleus. The alpha particles are the helium nucleus. The second type of decay is known as beta decay. During this decay there is release of positrons from the nucleus. The third type of decay is known as gamma decay. During this decay there is emission of gamma particles from the nucleus.

Note: The alpha particle contains two protons and two neutrons because the alpha particle is the helium nucleus. The two electrons are donated which gives the alpha particle a +2 charge. Protons are different from the alpha particles; they contain only one proton.