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The half-life of Uranium – $233$ is $160000$ years i.e., Uranium $233$ decays at a constant rate in such a way that it reduces to $50 %$ in $160000$ years. In how many years will it reduce to $25 %$ ?

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80000

years

240000

years

320000

years

40000

years

answer is C.

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Detailed Solution

It is given that the half-life of

U_{233}

= 160000

years.

∴

It becomes

50 %

of the original amount in

160000

years.
Now,

25 % =

\frac{1}{2} \times

50 %

i.e., another half-life is needed to reduce the original amount into

25 %

.
So, another

160000

years will reduce the original amount into

25 %

∴

The required number of years

= 160000 + 160000

\Rightarrow

Required number of years

= 320000

So, in

320000

years it will reduce to

25 %

.
Hence, the correct option is 3.

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The half-life of Uranium – 233 is 160000 years i.e., Uranium 233 decays at a constant rate in such a way that it reduces to 50% in 160000 years. In how many years will it reduce to 25%?

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

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The half-life of Uranium – $233$ is $160000$ years i.e., Uranium $233$ decays at a constant rate in such a way that it reduces to $50 %$ in $160000$ years. In how many years will it reduce to $25 %$ ?