Question

We know that radon is a radioactive element. An isotope of radon has a half-life of about four days. Ts means that at the end of each four-day period, one-half of the radon changes into another substance through radioactive decay. For example, if you started with 20 grams of radon, after four days, 10 grams would remain; after eight days, 5 grams would remain; and so on. How much will be left of 32 grams of radon after 20 days?

Answer 1

Given that :- At the end of each four days period one half of the radon changes into another substance .
then,
we have to find , how much will be left of 32 grams of radon after 20 days.

Now,
1st end of four days period radon left .one half the given radon
I.e ,. 1 st four days ---- 16 gm ( half of given amount of radon )

similarly ,
after first 8 days -left --- 8 gm .
after first 12 days left ----4 gm .
after first 16 days left ----- 2 gm
and , require days ( means after 20 days )
it left only one gram( 1 gm ) radon .

I hope u understand ... ?? ☺☺

Answer 2

Table of Content
Half-Life is the time taken for

Modern Half-Life formulae

How is half-life useful in carbon dating

Uses of the half-life in NDT

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According to the law giving quantitative description about radioactivity, the rate of disintegration decreases with a decrease in the number of atoms, i.e., when the number of atoms left behind is small, rate of disintegration also would have fallen considerably.We know that the nuclei of radioactive substances are unstable. They break down i.e. disintegrate into a completely new atom and this process is termed as radioactive decay. The radioactivity of an object is indeed measured by the number of nuclear decays it emits every second. Hence, the more it emits, the more radioactive the substance is.

The half-life of a radioactive substance, as the name suggests is the time taken for half its radioactive atoms to decay. Half-life of a radioactive substance is defined as the time during which the number of atoms of the substance are reduced to half their original value. It is not generally possible to predict when a particular atom will decay or not. However, with the help of half-life it becomes possible to calculate the time taken by half of the nuclei of radioactive substance to decay. There may be several definitions of half-life, but they basically imply the same thing.

Half-Life is the time taken for
Half-life is the time taken

The half-lives of different radioactive substances are different. We list below the half-lives of some of the known sample elements:

Isotope Half-life
Carbon-14 5,715 years
Francium-223 20 minutes
Oxygen 16 infinite
Uranium 238 4,460,000,000 years
Uranium 235 713,000,000 years
Cobalt 60 5.27 years
Silver 94 42 seconds
The figure given below further illustrates the concept of half-life. It shows the original substance and then what happens to it after it decays post one half-life and two half-lives.


Concept of Half Life

Modern Half-life formulae
The graph shows the decay curve for a radioactive substance. It shows the original substance and then what happens to it after it decays post one half-life and two half-lives. Radioactivity decreases with time. It is possible to find out the half-life of a radioactive substance from a graph of the count rate against time.

Graph of the Radioactive Substance

There are various ways of measuring half-life of substances. We give three main formulae to measure half-life:

N (t) = N0 e-t/τ

N (t) = N0 e -λt

Here,

N0 is the initial quantity of the substance that will decay,

N(t) is the quantity that still remains and has not yet decayed after a time t,

t1/2 is the half-life of the decaying quantity,

τ is a positive number which denotes the mean lifetime of the decaying quantity,

λ is a positive number called the decay constant of the decaying quantity.

A significant feature of the above graph is the time in which the number of active nuclei (N) is halved. This is independent of the starting value, N = N0. Let us compute this time:

N0/2 = N0e–λr'

= e–λr' = 1/2

or, λt' = In 2 = 0.693 (approx)

or, t' = T1/2 = 0.693/λ

This half-life represents the time in which the number of radioactive nuclei falls to 1/2 of its starting value. Activity, being proportional to the number of active nuclei, also has the same half-life.

Radioactive Decay Simulation