Half Life

This is the time taken for an atom to disintegrate half of its original
If N is the original mass or count rate.
After.
|Mass remain |mass lost/ mass decayed
One half life(1T). N/2. N/2
Two half life (2T). N/4. 3N/4
Three half life (3T). N/8. 7N/8
Four half life (4T). N/16. 15N/16

Formula Method

N/n = 2^ K
Original Mass/ mass remain = 2 index of K
n = mass remain, N = Original mass , K = constant, t = total time taken,
T= half life
Decay constant = In 2/T = 0.693/ T

Example: A sample of half life 5 years presently weighs 100N. It weighs in newton
20 years ago was.
Solution
Number of half life= 20years/ 5years = 4 half life
For 4 half life= N/16 remains
N/16 = 100
N= 16 x 100
N= 1600
Original mass= 1600 Newton

Second Method
t= 20 years , T = 5 years
K = t/ T = 20/5 = 4
N/ n = 2 ^ K
N/100 = 2 ^ 4
N/100 = 16
N= 16 x 100
N = 1600N
Original mass= 1600 Newton
Example: A radioactive substance of initial mass 8g has a half life of 10days. 7g of the
Substance have disintegrated after? Calculate the total time taken.
Solution
N= 8g , T= 10 days, t= ?
Mass lost= Original mass – mass remain
Mass lost = 8g – 7g = 1g
N/n = 2 ^ k
8/1 = 2^ k
2^ 3 = 2 ^ k
K= 3
From equation (2)
t = K T
t = 3 x 10 days
t = 30 days

Example: A substance with a half life of 5 minutes has the countrate of 500 after 15 minutes. The count rate at 0 time was
Solution
T = 5 minutes, n = 500 , t= 15 minutes
t = K T
15= K x 5
K = 3
N/n = 2 ^ 3
N/500 = 8
N= 500 x 8
N= 4000

Example: A radioactive substance with a half life of 5s has a decay constant of
Solution
Decay constant = 0.693/T
Decay constant= 0.693/5
Decay constant = 0.14/s

Example: A radio active has an initial activity of 7000 count/ sec and an activity of 875 count / sec after 6 hours.what is the half life
Solution
N= Original mass = 7000
t= 6 hours
n= 875
N/n = 2 ^ k
7000/ 875 = 2 ^ k
8 = 2 ^ k
2 ^ 3 = 2 ^ k
K = 3
t = K T
6 = 3 T
T= 6/3
T = 2 hours

What is Half life in Physics

Half Life

Formula Method

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Half Life

Formula Method

39 Comments