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Given initially 100 g of Plutonium-239, how muchtime must pass for amount to drop to1鈥塯 ?

Short Answer

Expert verified

The time taken is 160.18鈥塼丑辞耻蝉补苍诲鈥墆别补谤蝉.

Step by step solution

01

Given data

N0= 100鈥塯

N= 1鈥塯

02

Concept of Number of Nuclei which remain

The number of nuclei which remain after time t is given by:

N=N0e位迟 .

Where =顿别肠补测鈥塩辞苍蝉迟补苍迟=ln2T1/2 , N0 is the original number of nuclei, T1/2= half-life and N=is the number of nuclei at time t.

03

Calculate the time required from the Concept of the Number of Nuclei which remain

Plutonium 239's half-life is 24.11thousand years.

For nuclear decay, obtain:

N=N0e位迟=N0eln2T1/2t

Apply logarithm on both sides:

lnNN0=ln2tT1/2

Rearrange the above equation for t, substitute the values as:

t=T1/2ln2lnNN0=24.11鈥塼丑辞耻蝉补苍诲鈥墆别补谤蝉ln2ln1鈥塯100鈥塯=160.18鈥塼丑辞耻蝉补苍诲鈥墆别补谤蝉

Thus, the time taken is 160.18鈥塼丑辞耻蝉补苍诲鈥墆别补谤蝉.

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