First slide

Radio activity

Question

Uranium ores contain one radium 226 atom for every $2.8 x 10^{6}$ uranium 238 atoms. Calculate the half-life of ${}_{92}^{238}U$ given that the half-life of ${}_{88}^{226}R a$ is 1600
years ( ${}_{88}^{226}R a$ is a decay product of ${}_{92}^{238}U$ )

Moderate

A

$175 x 10^{6} y e a r s$
B

$1600 x \frac{238}{92} y e a r s$
C

$4.5 x 10^{9} y e a r s$
D

1600 years

Solution

$a t s t e a d y s t a t e N_{1} λ_{1} = N_{2} λ_{2} 2.8 x 10^{6} \frac{1}{T_{1}} = 1 \frac{1}{T_{2}} T_{2} = 1600 y e a r s T_{1} = 4.45 x 10^{9}$

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