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Answer 1 · 2016-03-02T19:36:15

#45"min"#

The equation for radioactive decay is:

#N_t=N_0e^(-lambda"t")#

#N_0# is the initial number of undecayed atoms.

#N_t# is the number of undecayed atoms after time #t#.

#lambda# is the decay constant.

We can say that #N_0# represents 100% of undecayed atoms.

If 34% decay then there must be 100 - 34 = 66% atoms remaining.

#:.66=100e^(-lambda"t")#

#:.ln66=ln100-lambda"t"#

#:.lambda"t"=ln100-ln66#

#:.lambda=(4.605-4.19)/27=0.0514"min"^(-1)#

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

#:.t_(1/2)=0.693/0.0514=45"min"#