Question

The isotope 208Tl undergoes β decay with a half-life of 3.1 minutes. What fraction of 208Tl will remain after 15.5 minutes?

a) 1/2
b) 1/4
c) 1/8
d) 1/16

Answer 1

After five half-lives, which amount to 15.5 minutes for isotope 208Tl with a half-life of 3.1 minutes, 1/32 of the original quantity of 208Tl will remain.

Step-by-step explanation:

The isotope 208Tl undergoes β (beta) decay with a half-life of 3.1 minutes. To find the fraction of 208Tl that will remain after 15.5 minutes, you divide the total time by the half-life to determine the number of half-lives that have passed and then apply the decay formula. In this case, 15.5 minutes divided by 3.1 minutes per half-life equals 5 half-lives.

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• After the first half-life, 1/2 of the original amount remains.
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• After the second half-life, 1/4 of the original amount remains.
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• After the third half-life, 1/8 of the original amount remains.
• 
  
• After the fourth half-life, 1/16 of the original amount remains.
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• After the fifth half-life, 1/32 of the original amount remains.

Therefore, the correct answer is that 1/32 of the original 208Tl will remain after 15.5 minutes.