Answer:
8.10 days
Explanation:
The half-life of gold-198 (2.70 days) is the time it takes for half the gold to decay.
After one half-life, half (50 %) of the original amount will remain.
After a second half-life, half of that amount (25 %) will remain, and so on.
We can construct a table:
No. of half-lives Fraction remaining
1 [tex]\frac{1}{2}[/tex]
2 [tex]\frac{1}{4}[/tex]
3 [tex]\frac{1}{8}[/tex]
Thus, the gold will decay to ⅛ of its original mass after three half-lives.
∴ Time required = 3 × 2.70 days = 8.10 days
Half-life is the period by which the substance gets reduced to it half of the concentration value. It will take 8.10 days for the 180 gm sample to reduce to one-eighth mass.
Half-life is the time taken by the concentration of the substance to get decreased to its half value compared to the initial value.
The time taken by the gold-198 to get reduced to its half concentration is 2.70 days. After a half-life, only 50% of the original value remains. Similarly, after the second half-life, 25% of the initial concentration will be left.
At the third half-life, one-eighth of the concentration will be remaining and hence the time is calculated as:
[tex]3 \times 2.70 = 8.10 \;\rm days[/tex]
Therefore, 8.10 days will be required to take 180 gms of original mass to get decayed.
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