# If a scientist purifies 10 gram of radium-226, how many years must pass before only 0.50 gram of the original radium-226 sample remains unchanged?

##### 1 Answer

Dec 26, 2017

The number of years is

#### Explanation:

The half life of

The radioactive constant is

The equation for radioactive decay is

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

Therefore,

#e^(-lambdat)=(N(t))/N_0=0.5/10=0.05# .

Taking natural logs of both sides,

#-lambdat=ln(0.05)#

#t=- (ln 0.05)/(lambda)#

#=- ln0.05/(ln2//t_(1//2))#

#=- ln0.05/ln2*t_(1//2)#

#=- ln0.05/ln2*"1599 years"#

#=# #" 6911years"#