If a 500.0 g sample of technetium-99 decays to 62.5 g of technetium-99 remaining in 639,000 years, what is the half-life of technetium-99?

It takes 2113000 years for a 500.0 g sample of technetium-99 decays to 62.5 g.    

Half Life:

It is the time in radioactive substance remains half of its initial concentration.

The initial amount of radioactive Technetium-99 present in the sample is  

= 500 g  

After 1 half life the remaining mass of the Technetium-99 is  

= 250 g  

After 2 half life the remaining mass of the Technetium-99  is  

= 125 g  

After 3 half life the remaining mass of the Technetium-99 is  

m = 62.5 g  

So after 3 half life the remaining Technetium-99 is 62.5 g.  

Thus,

Therefore, it takes 2113000 years for a 500.0 g sample of technetium-99 decays to 62.5 g.

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Half life of the sample is given as

Explanation:

As we know that radiactive substance becomes half in one half life time period

here we know that initial amount of radioactive substance present in the sample is

m = 500 g

After 1 half life the remaining mass of the sample is

m = 250 g

After 2 half life the remaining mass of the sample is

m = 125 g

After 3 half life the remaining mass of the sample is

m = 62.5 g

So the given time interval is equivalent to 3 half life

so we have