Question

Radium-223 id a radioactive isotope with a half-life of 11.4 days. Approximately how long will it take for the activity of a sample 223Ra to decease to 2.50% of its initial value

Answer 1

Answer:

It will take 61 days for the activity of a sample Ra-223 to decease to 2.50% of its initial mass.

Explanation:

Initial mass of the Radium-223= x

Final mass of the Radium-223 left after time t = 2.50% of x= 0.025x

Time taken by the sample = t

Half life of the Radium-223 = $t_{1/2}=11.4 days$

Formula used :

$N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

where,

$N_o$ = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

$t_{\frac{1}{2}}$ = half life of the isotope

$\lambda$ = rate constant

$0.025x=x\times e^{-(\frac{0.693}{11.4 days})\times t}$

$t=60.68 days\approx 61 days$

It will take 61 days for the activity of a sample Ra-223 to decease to 2.50% of its initial mass.