How much of 1kg sample of U-238 will be present after 500 million years? The half-life of U-238 is 4.5x10⁹ years

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• 0.926kg or 930 grams...check.

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  by WarHorseLeBron on August 7th, 2011

• Excel returns 992 gr to me.
  
  ????????

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  by Crowsnest on August 7th, 2011

• Im trying, as a mental exercise .....
  
  If I name; "h" the half-live period, M the mass, and t the time lapse .....
  I think I could write ...
  
  d(M)/d(t)= (M/2)/h : Rate of Mass change, with respect to rate of time change = Halve of the Initial Mass, divided by Half-live period.
  
  Working a little bit ....
  
  d(M)= (M/2h) d(t) --> d(M)/M= 1/2h d(t)
  
  Integration of both sides ...
  LN(M)= t/2h + C
  
  For a given h, and given initial Mass, constant C can be calculated, and the equation solved. As ..
  
  M =e^(t/2h+C)
  
  I think this expression looks logical and could better fit your numbers.
  
  Sorry but I have no time now for testing the numbers.
  
  I'd appreciate any comment or correction fom you.
  
  Regards

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  by Crowsnest on August 9th, 2011

• I think that the Mo (initial mass) will be inside the C constant, once solved.

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  by Crowsnest on August 9th, 2011

• I just plugged the numbers in your equation. It came out to 926g

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  by WarHorseLeBron on August 9th, 2011

• Oh ¡¡
  
  It fits better ¡
  
  Thanks a lot.

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  by Crowsnest on August 9th, 2011