What is half-life and its significance in Chemistry?
Half Life:
It is very important to know here that the concept of half life is a very vital subject when the chemists and scientists are dealing with those radioactive substances that have an unstable nucleus. Hence, it is an important task to study their half-life.
The prime objective of chemists is to deal with a variety of atoms, molecules, ions and isotopes. Among them some have very strong intramolecular bonding present among them and hence have a very solid and stable structure.
But on the other side, others are radioactive and are subjecting to regular decays at constant time intervals through distinctive forms of emissions.
With each passing day and time, the total weight of those radioactive substances will reduce to half and hence, that particular time that radioactive isotope will take to reduce half of its initial concentration named as half-life, It is worth mentioning here that after half life, if it is 8 days for a certain isotope, the amount of that radioactive substance will get reduced to 50% and after each interval the amount that present will be 25% and 12.5% respectively.
Moreover, it is very well written by scholars that radioactive isotopes have a very certain half life that is neither affected by the conditions and are independent to the initial amount of that particular substance present.
Calculation of Half Life:
Whenever we are studying the concept of half life in chemistry, it is very important to explore various methods by which we calculate half life. There are two methods to calculate the half life.
Method 1:
Method 1 states that the half life of any radioactive substance can be calculated by the formula given below
Amount Remaining= Initial Amount × (1/2) n
Where n is the number of half-lives over which we need to calculate the amount remaking.
Method 2:
The calculation of half life via this method is a relatively difficult task as two formulae are used in it. First of all, the value of the rate constant need to be calculated via
K=ln2/t1/2
The value of ln 2 is 0.6931 while t is the half-life of a particular substance. The second step after calculation of k is to calculate the amount of substance leftover and hence the below stated formula will use.
Af = Ao e-kt
= Final Concentration
Ao= Initial Concentration
K= constant
t= time
It is worth mentioning that the negative sign present in the formula states that the overall concentration of the radioactive substance will decay after the half life time has passed.
Example 1:
Iodine-131 has a half life of 8 days. If there are 200 grams of this sample present initially, then how much of Iodine 131 will remain after 32 days?
The example as stated earlier can solve by two methods. We will solve it via both techniques here and at the end, the answers will recheck to confirm the credibility of both formulae.
Method 1:
Amount Remaining= Initial Amount × (1/2) n
Amount Remaining= 200 g × (1/2) 4
so, Amount Remaining= 12.5 g
Note: the value of n here is 4 because we need to calculate the final amount that has asked after 32 days which is 32/8= 4 half lives.
Related: For calculating the atomic weight of elements, you may try the atomic weight calculator.
Method 2:
K=ln2/t1/2
K=ln2/8
K=0.0866
Af = Ao e-kt
Af = 200 e-(0.08644) (32)
Af = 12.5 g
Hence, the final amount that will be present at the end of the said time will be 12.5 grams by both methods.
Example 2:
Sodium-24 has a half-life of 15 hours. If there are 800g of Na-24 initially, how long will it take for 750 g of Na-24 to decay.
K=ln2/t1/2
K=ln2/15
K=0.0461
Now we need to calculate the time it will take to decay of 750 grams.
Af = Ao e-kt
ln (Af/Ao) =-kt
Af which is the final amount left will be 50 grams in the current example as 800 g is the total initial amount and 750 g will decay after a certain time.
ln (50/800) =-0.0461t
-2.722/-0.0461= t
t= 60 h.
Hence, sodium-24 will take 60 h to decay its 750 g and at the end of 60 h, the amount of Na-24 that will left behind will calculate as 50 grams.