question archive A container holds a pure sample of a radioactive substance with a half-life of 2 hours
A container holds a pure sample of a radioactive substance with a half-life of 2 hours
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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?
a) After 1 hour, less than 50\% of the original atoms in the container will have decayed.
b) 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\%.
Answer: A and C
In addition to the sample mentioned in Part A, consider a pure sample of a different radioactisubstance that has a half-life of 1 hour. Assume that you initially have twice as many atoms of this new sample as you have of the previous sample. The table below summarizes this information:
Sample Half-life (hours) Original number of atoms
A 2 N_0
B 1 2N_0
Part B
Which of the following statements about samples A and B are true?
a) After 1 hour, a larger percentage of undecayed atoms will be left in sample A than in sample B.
b) After 1 hour, a larger number of atoms will have decayed in sample B than in sample A.
c) After 2 hours, the same number of atoms will have decayed in both samples.
d) After 2 hours, both samples will have the same number of undecayed atoms.
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a (the half life is 2 hours so only at 2 hours 50% of atoms woulds have decayed not before)
c ( definition of half -life:time required for 50% of the atoms to decay)
for part 2
b(after 1 hour the no. of undecayed atoms in sample B will be N_0 where as this the total no. of atoms of sample A present during the start, some will be decayed by now.)
d (after 2 hours sample B would have gone through 2 half lives with 0.5 N_0 atoms remaining
where as sample A would have gone through 1 half cycle with 0.5 N_0 atoms remaining.
so same no. of atoms remaining)
