The half-life of radium is 1600 , text{years} | vedclass

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(D) The formula for radioactive decay is $N = N_0 \left( \frac{1}{2} ight)^n$, where $n$ is the number of half-lives.Given $N_0 = 100 \, 	ext{g}$ a

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$3200$

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(D) The formula for radioactive decay is $N = N_0 \left( \frac{1}{2} ight)^n$, where $n$ is the number of half-lives.Given $N_0 = 100 \, 	ext{g}$ and $N = 25 \, 	ext{g}$.Substituting the values: $\frac{25}{100} = \left( \frac{1}{2} ight)^n$.$\frac{1}{4} = \left( \frac{1}{2} ight)^n \Rightarrow \left( \frac{1}{2} ight)^2 = \left( \frac{1}{2} ight)^n$.Thus, $n = 2$.The total time $t$ is given by $t = n 	imes T_{1/2}$.$t = 2 	imes 1600 \, 	ext{years} = 3200 \, 	ext{years}$.

The half-life of radium is $1600 \, \text{years}$. After how many years will $25 \, \text{g}$ of radium remain from $100 \, \text{g}$ of radium?

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