Answer

Verified

88.8k+ views

**Hint:**Half-Life as the name suggests it is the required time interval for a radioactive sample to decay to its one-half. It can also be stated as the required time interval that is needed for a number of radioactive disintegration each second of a radioactive material to get to its one-half.

**Complete step by step solution:**

Find the Half-Life:

$N\left( t \right) = {N_o}{\left( {\dfrac{1}{2}} \right)^{\dfrac{t}{{{t_{1/2}}}}}}$;

Here:

$N\left( t \right)$= Quantity of the Substance remaining;

${N_o}$ = Quantity of the original substance;

t = Time elapsed;

${t_{1/2}}$= Half – Life.

Put in the given values:

$\left( {\dfrac{1}{{16}}} \right){N_o} = {N_o}{\left( {\dfrac{1}{2}} \right)^{\dfrac{2}{{{t_{1/2}}}}}}$;

Cancel out the common factors:

$ \Rightarrow \left( {\dfrac{1}{{16}}} \right) = {\left( {\dfrac{1}{2}} \right)^{\dfrac{2}{{{t_{1/2}}}}}}$;

Make the base on the LHS to the RHS and compare their powers:

$ \Rightarrow {\left( {\dfrac{1}{2}} \right)^4} = {\left( {\dfrac{1}{2}} \right)^{\dfrac{2}{{{t_{1/2}}}}}}$;

Do the needed mathematical Calculations:

$ \Rightarrow \dfrac{2}{{{t_{1/2}}}} = 4$;

So, the half-life would be:

$ \Rightarrow 2 = 4 \times {t_{1/2}}$;

$ \Rightarrow {t_{1/2}} = \dfrac{1}{2}$;

In terms of minutes;

${t_{1/2}} = 30\min $;

**The half-life of the sample is 30min.**

**Additional information:**

There are various types of radioactive decays available such as Alpha decay, Beta-Decay and Gamma Decay. These decays happen due to the instability in the nucleus of an atom. The more unstable the nucleus the higher would be the energy of radioactive decay. The lowest level of energy decay is in alpha decay, Beta decay has higher energy decay than alpha decay and in the Gamma decay it is the highest.

**Note:**Here the quantity of the substance remaining is one sixteenth of the original substance and we have given the time elapsed as 2 hours. Here apply the formula for Half-Life and calculate the known variable.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

A passenger in an aeroplane shall A Never see a rainbow class 12 physics JEE_Main

Velocity of car at t 0 is u moves with a constant acceleration class 11 physics JEE_Main