document.write( "Question 1204528: If 250 mg of a radioactive element decays to 190 mg in 36hrs find the half-life of the element \n" ); document.write( "

Algebra.Com's Answer #840830 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "If 250 mg of a radioactive element decays to 190 mg in 36hrs find the half-life of the element.
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document.write( "The formula for the decay mass in terms of half-life is\r\n" );
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document.write( "    M(t) = ,    (1)\r\n" );
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document.write( "where t i the time; T is the half-life time, M(t) is the current remaining mass;  is initial mass.\r\n" );
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document.write( "We are given   = 250 mg;  t = 36 hours.;  M(t) = 190 mg;    We need to fint half-life T.\r\n" );
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document.write( "The basic equation (1) takes the form\r\n" );
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document.write( "    190 = .\r\n" );
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document.write( "Divide both sides by 250.  You will get\r\n" );
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document.write( "     = \r\n" );
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document.write( "or\r\n" );
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document.write( "    0.76 = .\r\n" );
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document.write( "Take logarithm base 10 of both sides\r\n" );
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document.write( "    log(0.76) = .\r\n" );
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document.write( "Express T\r\n" );
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document.write( "    T =  = calculate and get = 90.9255 hours = 90 hours and 53 minutes (approximately).\r\n" );
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document.write( "ANSWER.  Half-life is about 90 hours and 53 minutes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On radioactive decay, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Radioactive decay problems \r
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\n" ); document.write( "\n" ); document.write( "You will find many similar (and different) solved problems there.\r
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\n" ); document.write( "\n" ); document.write( "Use this lesson as your handbook, textbook, guide, tutorials, and (free of charge) home teacher.\r
\n" ); document.write( "\n" ); document.write( "Learn the subject from there once and for all.\r
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