A) 1580 yr
B) 3160 yr
C) 4740 yr
D) 6320 yr
Correct Answer: D
Solution :
Key Idea: Use the following formula to find the time required to reduce it to 1/16. \[N={{N}_{0}}\times {{\left( \frac{1}{2} \right)}^{n}}\] where N = amount left \[=\frac{1}{16}\] \[{{N}_{0}}=\]initial amount = 1 \[n=\]number of half-lives \[\therefore \] \[\frac{1}{16}=1\times {{\left( \frac{1}{2} \right)}^{n}}\] or \[{{\left( \frac{1}{2} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\therefore \] \[n=4\] Time required to complete given number of half-life \[={{t}_{1/2}}\times n\] \[=1580\times 4=6320\,yr\] \[\therefore \] Radium will become \[\frac{1}{16}\]after 6320 yr. Alternate method| Initial amount | Amount left After one half-life | Time taken |
| 1 | 1/2 | 1580 yr |
| 1/2 | 1/4 | 1580 yr |
| 1/4 | 1/8 | 1580yr |
| 1/8 | 1/16 | 1580 yr |
| 6320 yr |
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