The half-life of strontium-90 is 28 years. How long will it take a 30-mg sample to decay to a mass of 21.6 mg? (Round your answer to the nearest whole number.)

Answer 1

21.6 = (30)(0.5)^t/28

0.95333 = (0.5)^t/28

ln 0.95333 = (t/28) ln 0.5

Can you solve for t and answer?

Answer 2

Hi Emily R.,

There's nothing wrong with Mark M.'s answer above.

But, let me add a little perspective,as a chemist! First, the given value is wrong for Sr(⁹⁰) decay half-life -- it's 28.79 years (about) which should have been rounded to 29 years. You can never get a reliable answer from incorrect initial data -- your calculation would be flawed (by determinate error) from the start. When you round off your answer, there has been rounding twice -- once in the initial data, and once after the calculation -- one form of "double rounding". Scientifically, legally, and mathematically this is a bad idea. So if you are ever in a position of responsibility for your results in the world, please remember to check your input data carefully!!!

Second, how would you know when you reach 21.6 mg of Sr(⁹⁰)? The decay, via Y(⁹⁰) to Zr(⁹⁰), doesn't significantly change the mass of the sample sitting in front of you -- you would have to do a chemical separation, or perhaps mass-spectrometry, to find out.

Now for the good news, comparatively: this isotope is does not disperse widely following a radioactive spill, though it is generated in substantial amounts in a deliberate fission-bomb explosion. Iodine and cesium isotopes are more problematic (see http://www.radioactivity.eu.com/site/pages/Strontium_90.htm ).

-- Cheers, Mr. d.

P.S. I find it hilarious that the Video Answer option that I see above says "In Beta Testing", since the two radio-decays above both generate beta-rays!