A container holds a pure sample of a radioactive substance with a half-life of 2

Question

A container holds a pure sample of a radioactive substance with a half-life of

2 hours.

Part A

Which of the following statements are true?

Check all that apply.

a.) After 1 hour, less than 50% of the original atoms in the container will have decayed. b.) OK After 1 hour, more than 50% of the original atoms in the container will have decayed. c.) After 2 hours, 50% of the original atoms in the container will have decayed. d.) After 4 hours, 25% of the original atoms will have decayed. e.) After 4 hours, the total number of atoms in the container will be reduced by 75%.

Explanation / Answer

Half life period means half of the initial amount will be remaining after decay which is the same as half of the initial amount is decayed.
Nt= N0 *1/2 ^ (t/th)

After one hour Nt = N0 *? 0.5 ^ (1/2) =0.7 N0 remaining or 0.3 has decayed
Hence it is TRUE that
After 1, less than 50 %of the original atoms in the container will have decayed

But the statement
After 1 hours, more than 50% of the original atoms in the container will have decayed is false.
======================================...
After 2 hours
Nt= *0.5 ^ (2/2) N0= 0.5 N0 is remaining and 0.5 of N0 has decayed.

Hence it is TRUE that
After 2 hours, 50% of the original atoms in the container will have decayed.
======================================...
After 4 hours
Nt= 0.5 ^ (4/2) N0= 0.5^2 N0 = 0.25 N0 is remaining or 0.75N0 has decayed.
Hence it is false that
After 4 hours, 25 %of the original atoms will have decayed and
After 4 hours, 25 %of the original atoms will have decayed
======================================...

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