A radioactive sample of half-life 10 days, contains 1000x nuclei. Number of original nuclei present after 5 days is

Question

A radioactive sample of half-life 10 days, contains 1000x nuclei. Number of original nuclei present after 5 days is (A) 707x (B) 750x  (C) 500x  (D) 250x

Tardigrade Admin · Accepted Answer

The number of radioactive nuclei left after n half lives is N=(N0/2n) for 5 days n=(1/2) So, N=(1000 x/2(1)2)=(1000 x/√2) =(1000 x/1.414)=(0.707)1000x =707x

Q. A radioactive sample of half-life $10$ days, contains $1000 x$ nuclei. Number of original nuclei present after $5$ days is

$707 x$

$750 x$

$500 x$

$250 x$

The number of radioactive nuclei left after n half lives is
$N = \frac{N _{0}}{2 ^{n}}$

$f or 5 d a ys n = \frac{1}{2}$
So, $N = \frac{1000 x}{2 ^{\frac{1}{2}}} = \frac{1000 x}{2}$
$= \frac{1000 x}{1.414} = (0.707) 1000 x$
$= 707 x$

Q. A radioactive sample of half-life 10 days, contains 1000x nuclei. Number of original nuclei present after 5 days is

707x

750x

500x

250x