(C) The radioactive decay formula is given by $N = N_o (1/2)^n$,where $n$ is the number of half-lives.Given that after $3160 \ years$,the remaining am

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(C) The radioactive decay formula is given by $N = N_o (1/2)^n$,where $n$ is the number of half-lives.Given that after $3160 \ years$,the remaining amount $N = (1/4)N_o$,so $N/N_o = 1/4$.Substituting this into the formula: $1/4 = (1/2)^n$.Since $1/4 = (1/2)^2$,we get $n = 2$.The number of half-lives $n$ is related to total time $t$ and half-life $t_{1/2}$ by $n = t / t_{1/2}$.Therefore,$2 = 3160 / t_{1/2}$.$t_{1/2} = 3160 / 2 = 1580 \ years$.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

Medium

$^{226}Ra$ disintegrates at such a rate that after $3160 \ years$ only one-fourth of its original amount remains. The half-life of $^{226}Ra$ will be .......... $years$.

A
$790$
B
$3160$
C
$1580$
D
$6230$

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Nuclear Chemistry

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Rate of decay and Half-life

The half-life period of a radioactive substance is $140 \ days$. After how much time will $15 \ g$ decay from a $16 \ g$ sample of it?

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The half-life of a radioactive element is $100 \, \text{min}$. The time interval between the stages of $50\%$ and $87.5\%$ decay will be ...... $\text{min}$.

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The half-life of the radioactive isotope tritium $(_1^3H)$ is $12.3 \ years$. If the initial amount of tritium is $32 \ mg$,how many milligrams will remain after $49.2 \ years$ (in $mg$)?

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The half-life of a radioactive isotope is $3 \ hours$. If the initial mass of the isotope were $256 \ g$,the mass of it remaining undecayed after $18 \ hours$ would be ....... $g$. (in $.0$)

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$A$ radioactive isotope has a half-life of $20 \ days$. If $100 \ g$ of the substance is taken,the weight of the isotope remaining after $40 \ days$ is ......... $g$.

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$^{226}Ra$ disintegrates at such a rate that after $3160 \ years$ only one-fourth of its original amount remains. The half-life of $^{226}Ra$ will be .......... $years$.

Similar Questions

The half-life period of a radioactive substance is $140 \ days$. After how much time will $15 \ g$ decay from a $16 \ g$ sample of it?

The half-life of a radioactive element is $100 \, \text{min}$. The time interval between the stages of $50\%$ and $87.5\%$ decay will be ...... $\text{min}$.

The half-life of the radioactive isotope tritium $(_1^3H)$ is $12.3 \ years$. If the initial amount of tritium is $32 \ mg$,how many milligrams will remain after $49.2 \ years$ (in $mg$)?

The half-life of a radioactive isotope is $3 \ hours$. If the initial mass of the isotope were $256 \ g$,the mass of it remaining undecayed after $18 \ hours$ would be ....... $g$. (in $.0$)

$A$ radioactive isotope has a half-life of $20 \ days$. If $100 \ g$ of the substance is taken,the weight of the isotope remaining after $40 \ days$ is ......... $g$.

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