The time taken for 0.240 mole sample of radiuim to decay to 1.88×10¯³ mole is 79.8 days
We'll begin by calculating the number of half-lives that has elapsed.
Original amount (N₀) = 0.240 mole
Amount remaining (N) = 1.88×10¯³ mole
N = 1/2ⁿ × N₀
1.88×10¯³ = 1/2ⁿ × 0.240
Cross multiply
1.88×10¯³ × 2ⁿ = 0.240
Divide both side by 1.88×10¯³
2ⁿ = 0.240 / 1.88×10¯³
2ⁿ = 128
2ⁿ = 2⁷
Thus, 7 half-lives has elapsed
Number of half-lives (n) = 7
Half-life (t½) = 11.4 days
t = n × t½
t = 7 × 11.4
Therefore, the time taken for 0.240 mole sample of radiuim to decay to 1.88×10¯³ mole is 79.8 days
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