Question

96g of a radioactive substance undergoes radioactive decay. If its half life is 24 years then the amount of substance remaining after 96 years​??
A. 6g
B. 3g
C. 12g
D. 24g

Answer 1

Given :

Half life of radioactive substance = 24yrs

Mass of substance = 96g

To Find :

Amount of substance remaining after 96yrs

Solution :

★ Half life : The time required for any property (concentration or mass) to decrease by half is called half life.

First we need to find total number of half life in the given interval of time$.$

→ t = n × T(1/2)

• t denotes total time
• n denotes no. of half lives
• T(1/2) denotes half life

→ 96 = n × 24

→ n = 4

★ Fraction of substance left undecayed after n half life is given by

➠ N'/N = (1/2)ⁿ

➠ N'/96 = (1/2)⁴

➠ N' = 96/16

➠ N' = 6g

∴ 6g of radioactive substance will remain after 96yrs.