Half-life

Half Life

• radioactive nuclei of an element decay at a characteristic, constant rate
• the time it takes for half of radioactive sample to decay
• number of radioactive nuclei remaining is halved after each half life
• different isotopes have different half lives

Half-life Equation

• Mf=mi(1/2)n
• n=ttot
• t1/2
• Mf= final mass
• mi= initial mass
• n= number of half lives

Half-life Example 1

• How much of a 100.0 g sample of Au is left after 8.10 days if its half-life is 2.70 days?
• answer: 12.5g
• mf= ?
• mi= 100.og
• ttot= 8.10 days
• t1/2= 2.70 days
• n= 3 days
• n=ttot 8.10 days =3 days
• t1/2 2.70 days
• mf=100.0g(1/2)3 100.0g x 0.125 =12.5g

Example 2

• A 50.0 g sampler of N decays to 12.5 g in 14.4 seconds. What is its half life?
• answer: 7.2g
• mi=50.0g
• mf=12.5g
• ttot= 14.4 sec
• t1/2=?
• n=2
• 50.0 g
• 25.0g 1
• 12.5g 2 n=ttot t1/2=ttot 14.4 sec t1/2= 7.2g
• t1/2 n 2

Example 3

• There are 5.0 g of I left after 40.35 days. How many grams were in the original sample if its half-life is 8.07 days?
• answer: 160 g
• mf= 5.0 g
• mi= ?
• t1/2= 8.07 days
• ttot= 40.35 days
• n= 5 dyas
• n=40.35 days n=5 days mf=mi(1/2)n
• 8.07 days mi=mf 5.0g 5.0g
• (1/2)n (1/2)5 0.03125
• mi= 160g