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, $T_{0.5}$ = 19.7 minutes

$T_{0.5}= \frac{0.693}{\lambda} \\ \\ \Rightarrow \lambda= \frac{0.693}{T_{0.5}} \\ \\ \Rightarrow \lambda= \frac{0.693}{19.7} =0.035\ min^{-1}$

A₀ = 1g
t = 78.4 second
A = ?

$A = A_oe^{-\lambda t}\\ \\ \Rightarrow A = 1 \times e^{-0.035 \times 78.4}\\ \\ \Rightarrow A =0.064\ g$

After 78.4 minute, 0.064g 214Bi will be left.

Answer 2

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Half life, $T_{0.5}$ = 19.7 minutes

$T_{0.5}= \frac{0.693}{\lambda} \\ \\ \Rightarrow \lambda= \frac{0.693}{T_{0.5}} \\ \\ \Rightarrow \lambda= \frac{0.693}{19.7} =0.035\ min^{-1}$

A₀ = 1g

t = 78.4 second

A = ?

$A = A_oe^{-\lambda t}\\ \\ \Rightarrow A = 1 \times e^{-0.035 \times 78.4}\\ \\ \Rightarrow A =0.064\ g$

After 78.4 minute, 0.064g 214Bi will be left.

HOPE SO IT WILL HELP........