# If the radon concentration has become 1/20th of what it started as, and its half-life is 3.8 days, what amount of time in days has passed?

##### 1 Answer

Dec 24, 2017

The time is

#### Explanation:

The half life of Radon is

The radioactive constant is

The equation for radioactive decay is

#(N(t))/(N_0)=e^(-lambdat)#

Therefore,

#e^(-lambdat)=(N(t))/N_0=1/20# .

Taking natural logs of both sides,

#-lambdat=ln(1/20)=-ln20#

#t= (ln 20)/(lambda)#

#= ln20/(ln2//t_(1//2))#

#= ln20/ln2*t_(1//2)#

#= ln20/ln2*"3.8 days"#

#=# #"16.4 days"#