Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half - lives can be found by using the expression 3-t.
(a) What fraction of substance remains after 7 half-lives?
(b) After how many half-lives will the fraction be 1/243 of the original?
Solution:
Given, the fraction of the quantity that remains after t half-lives can be found by using the expression 3-t.
(a) We have to find the fraction of substance that remains after 7 half-lives.
According to the question,
Fraction of substance that remains after 7 half-lives = 3⁻⁷
Using law of exponents,
a⁻ⁿ = 1/aⁿ
So, 3⁻⁷ = 1/3⁷
Therefore, the required fraction is 1/3⁷.
(b) We have to find the half-lives in which the fraction will be 1/243.
According to the question,
3-t = 1/243
Now, 1/3t = 1/243
We know, 243 = 3⁵
1/3t = 1/3⁵
Therefore, the required half life is 5.
✦ Try This: Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half - lives can be found by using the expression 3-t.
(a) What fraction of substance remains after 8 half-lives?
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 140
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half - lives can be found by using the expression 3-t. (a) What fraction of substance remains after 7 half-lives, (b) After how many half-lives will the fraction be 1/243 of the original?
Summary:
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half - lives can be found by using the expression 3-t. (a) 1/3⁷ fraction of substance remains after 7 half-lives, (b) After 5 half-lives the fraction will be 1/243 of the original.
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