Question

For 214Bi, the half-life period is 19.7 minutes. Calculate the radioactive decay constant. Also calculate how much of 1 gram sample of 214Bi will remain after 78.4 minutes.

Answer 1

half life = 19.7 minutes

$t_{\frac{1}{12}}=\frac{ln\ 2}{\lambda}\\ \\ \Rightarrow 19.7 = \frac{ln\ 2}{\lambda}\\ \\ \Rightarrow \lambda = \frac{ln\ 2}{19.7}\\ \\ \Rightarrow \lambda = \frac{0.693}{19.7}\\ \\ \Rightarrow \lambda = 0.0351\ Bq$

So decay constant is 0.0351 Bq.

half life = 19.7 minutes
number of half lives in 78.4 minutes = 78.4/19.7 = 4
initial amount (N₀)= 1g
let after 4 half lives, remaining will be = $N_4$

$N_4= \frac{N_0}{2^4} = \frac{1}{16}\ g$

So after 78.4 minutes, $\frac{1}{16}$ g 214Bi will be remaining.

Answer 2

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half life = 19.7 minutes

$t_{\frac{1}{12}}=\frac{ln\ 2}{\lambda}\\ \\ \Rightarrow 19.7 = \frac{ln\ 2}{\lambda}\\ \\ \Rightarrow \lambda = \frac{ln\ 2}{19.7}\\ \\ \Rightarrow \lambda = \frac{0.693}{19.7}\\ \\ \Rightarrow \lambda = 0.0351\ Bq$

So decay constant is 0.0351 Bq.

half life = 19.7 minutes

number of half lives in 78.4 minutes = 78.4/19.7 = 4

initial amount (N₀)= 1g

let after 4 half lives, remaining will be = $N_4$

$N_4= \frac{N_0}{2^4} = \frac{1}{16}\ g$

So after 78.4 minutes, $\frac{1}{16}$ g 214Bi will be remaining.

HOPE SO IT WILL HELP.....