A physicist starts out with 320 grams of a radioactive element $Z$ and after 20 minutes he has only 20 grams left. What is the half-life of the element $Z$ ?

2 minutes

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3 minutes

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4 minutes

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5 minutes

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Solution

The correct option is D 5 minutes
The 320 grams of the radioactive element Z is reduced to 20 grams in 20 min.

$\Rightarrow$ Amount of Z reduced by $\frac{1}{16}$ times in 20 min.

It has completed 4 half-life as $\frac{1}{16} = \frac{1}{{(2)}^{4}}$

$∴$ Time of 4 half lives $= 20 m i n$

1 half-life period $= 5 m i n$

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Similar questions

5

32

= 0

Time 't' in minutes	$0$	$5$	$10$	$15$	$20$	$25$
Amount of radioactive element left in grams	$32$

15

50

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