Sample #1 is made from an isotope with decay constant
And sample #2 is made from an isotope with decay constant
,where
)Which of the following statements must be true?
A)The activity of sample #2 is greater than that of sample #1.
B)The activity of sample #1 is greater than that of sample #2.
C)The half-life exhibited for sample #1 is greater than that of sample #2.
D)The half-life exhibited for sample #2 is greater than that for sample #1

Question

Sample #1 is made from an isotope with decay constant 
And sample #2 is made from an isotope with decay constant 
,where 
)Which of the following statements must be true?
A)The activity of sample #2 is greater than that of sample #1. 
B)The activity of sample #1 is greater than that of sample #2. 
C)The half-life exhibited for sample #1 is greater than that of sample #2. 
D)The half-life exhibited for sample #2 is greater than that for sample #1

Quizplus · Accepted Answer

The decay constant is inversely proportional to the half-life, so the higher decay constant implies a shorter half-life. Since the decay constant of sample #2 is higher than that of sample #1, the half-life of sample #2 is shorter than that of sample #1. Thus, the correct answer is D. Also, the activity of a radioactive sample is directly proportional to its decay constant, so sample #2 has a higher activity than sample #1. Therefore, statement A is also true.

Sample #1 Is Made from an Isotope with Decay Constant