How do you find the half life of uranium-235? I tried to do 235 / 2 = 117.5 but that is wrong please help

half life is when you half/divide a number by 2 does this necessary mean that you divide or do you have to work out something else before dividing?

1 Answer
Mar 23, 2017

Answer:

Please see the explanation.

Explanation:

To find the half-life of any radioactive substance, you need to start with an initial mass of the substance, #Q(0)#, then, after a time interval ,t, you carefully measure the mass of the substance, Q(t)

The decay of radio active substances follow this equation:

#Q(t) = Q(0)e^(lambdat)#

Both #Q(0) and Q(t)# are in the same units of mass so this means that the exponential us unit-less (as it should be)

Let's solve for #lambda#.

#(Q(t))/(Q(0))= e^(lambdat)#

#ln((Q(t))/(Q(0)))= lambdat#

#lambda = ln((Q(t))/(Q(0)))/t#

Please notice that #lambda# must be in #"time units"^-1#, because t is in time units.

Now suppose that you are given a value for #lambda# and you want to know the time, #t_"half-life"#. (Which is defined as the time that it takes for half of the original quantity to decay.)

#(Q(t_"half-life"))/(Q(0))= e^(lambdat_"half-life")#

We know that the left side is #1/2#

#1/2= e^(lambdat_"half-life")#

#ln(1/2) = lambdat_"half-life"#

#-ln(2) = lambdat_"half-life"#

#t_"half-life"= -ln(2)/lambda#

Suppose that you are given the half-life and you need to find #lambda#

#lambda = -ln(2)/t_"half-life"#

The half-life for #U_235# is #7.04xx10^8" years"#

For #U_235#, #lambda = -9.84xx10^-10" years"^-1#