The percent of a present amount of radioactive radium after 100 years is 95.76%
Radium:
Radium is a chemical element with the symbol Ra. It is the sixth element in the Group 2 of the periodic table. Pure radium is silvery-white in color, but it combines with nitrogen readily on exposure to air and forms a black surface layer of radium nitride.
Here we have to find the percent of the present amount of radioactive radium remains after 100 years.
As we know:
y = a[tex]e^{-bt}[/tex]
y = a (at t =0)
as half-life:
0.5a = a[tex]e^{1600b}[/tex]
ln 0.5 = -1699b
b = -log 0.5/ 1600
Now model is:
y = a[tex]e^{log 0.5/1600 t}[/tex][tex]e^{log 0.5 / 1600 t}[/tex]
at t = 100
y = 0.95768
So there will be 95.76% radioactive radium after 100 years.
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