The half-life of radium is 1600 years. The time does 1g of radium take to reduce to 0.125g is

Question

The half-life of radium is 1600 years. The time does 1g of radium take to reduce to 0.125g is (A) 4800 years (B) 4500 years (C) 5000 years (D) 4750 years

Tardigrade Admin · Accepted Answer

Nuclear reactions are Ist order reaction (N/N0)=((1/2))n ⇒ (0.125/1)=(. (1/2) .)n =(1/8)=(1/2n) ⇒ n=3 n=(t/t(1)2) ; ∵ 3=(t/1600) t=4800

Q. The half-life of radium is 1600 years. The time does 1g of radium take to reduce to 0.125g is

4800 years

4500 years

5000 years

4750 years

Nuclear reactions are I^st order reaction
$\frac{N}{N _{0}} = (\frac{1}{2})^{n}$
$\Rightarrow \frac{0.125}{1} = (\frac{1}{2})^{n}$
$= \frac{1}{8} = \frac{1}{2 ^{n}}$
$\Rightarrow n = 3$
$n = \frac{t}{t _{\frac{1}{2}}}$ ;
$∵ 3 = \frac{t}{1600}$
$t = 4800$

Q. The half-life of radium is 1600 years. The time does 1g of radium take to reduce to 0.125g is

4800 years

4500 years

5000 years

4750 years

Nuclear reactions are Ist order reaction N0​N​=(21​)n ⇒10.125​=(21​)n =81​=2n1​ ⇒n=3 n=t21​​t​ ; ∵3=1600t​ t=4800

Nuclear reactions are I^st order reaction
$\frac{N}{N _{0}} = (\frac{1}{2})^{n}$
$\Rightarrow \frac{0.125}{1} = (\frac{1}{2})^{n}$
$= \frac{1}{8} = \frac{1}{2 ^{n}}$
$\Rightarrow n = 3$
$n = \frac{t}{t _{\frac{1}{2}}}$ ;
$∵ 3 = \frac{t}{1600}$
$t = 4800$