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Chapter 10: Q. 446 (page 1066)

The half-life of radioactive iodine is 60 days. How much of a 50 mg sample will be left in 40 days?

Short Answer

Expert verified

The amount left in 40 days will be79.37mg.

Step by step solution

01

Step 1. Given information

Half-life of iodine =60days

Initial sample =50mg

Time for decay=40days

02

Step 2. Writing the concept.

An amount A0that grows or decays at rate k for certain time t, will be given by:

03

Step 3. Calculation

Put the values of respective variables in the given formula:

A=2A0t=602A0=A0e60ke60k=2A0A0e60k=2Takinglogarithmbothsides.lne60k=ln260k.lne=ln2k=ln260NowsubstituteA0=50,t=40A=50e40.160ln2=50e23ln2=79.37mg

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