In a radioactive substance at t = 0, the number of atoms is 8 × 104 , its half-life period is 3 yr. the number of atoms 1 × 104 will remain after interval

Question

In a radioactive substance at t = 0, the number of atoms is 8 × 104 , its half-life period is 3 yr. the number of atoms 1 × 104 will remain after interval (A) 9 yr (B) 8 yr (C) 6 yr (D) 24 yr

Tardigrade Admin · Accepted Answer

By formuia, N = N0 ((1/2) )t/T or 104 = 8 × 104 ((1/2) )t/3 or ((1/8) ) = ((1/2) )t/3 or ((1/2) )3 = ((1/2) )t/3 ⇒ 3 = (t/3) Hence, t = 9 yr

Q. In a radioactive substance at t = 0, the number of atoms is $8 \times 1 0^{4}$ , its half-life period is 3 yr. the number of atoms $1 \times 1 0^{4}$ will remain after interval

9 yr

8 yr

6 yr

24 yr

By formuia, $N = N_{0} (\frac{1}{2})^{t / T}$
or $1 0^{4} = 8 \times 1 0^{4} (\frac{1}{2})^{t /3}$
or $(\frac{1}{8}) = (\frac{1}{2})^{t /3}$
or $(\frac{1}{2})^{3} = (\frac{1}{2})^{t /3}$
$\Rightarrow 3 = \frac{t}{3}$
Hence, $t = 9 yr$

Q. In a radioactive substance at t = 0, the number of atoms is 8×104 , its half-life period is 3 yr. the number of atoms 1×104 will remain after interval