The half-life of cobalt-60 is 5.27 years. Approximately how much of a 199 g sample will remain after 20 years?

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Answer 1 · 2016-04-18T16:08:36

#14.3"g"#

The expression for radioactive decay is:

#N_t=N_0e^(-lambdat)#

#N_0# is the initial number of undecayed atoms.

#N_t# is the number of undecayed atoms remaining at time #t#

#lambda# is the decay constant

The relationship between #lambda# and the half - life #t_(1/2)# is:

#lambda=0.693/t_(1/2)#

#:.lambda=0.693/5.27=0.1315"a"^(-1)#

Taking natural logs of both sides of the decay expression #rArr#

#lnN_t=lnN_0-lambdat#

#:.lnN_t=ln199-(0.1315xx20)#

#lnN_t=5.293-2.63=2.66#

From which:

#N_t=14.29"g"#