Hello!
The half-life is the time of half-disintegration, it is the time in which half of the atoms of an isotope disintegrate.
We have the following data:
mo (initial mass) = 10 g
m (final mass after time T) = ? (in g)
x (number of periods elapsed) = ?
P (Half-life) = 30 seconds
T (Elapsed time for sample reduction) = 1 minute → 60 seconds
Let's find the number of periods elapsed (x), let us see:
[tex] T = x*P [/tex]
[tex] 60 = x*30 [/tex]
[tex] 60 = 30\:x [/tex]
[tex] 30\:x = 60 [/tex]
[tex] x = \dfrac{60}{30} [/tex]
[tex] \boxed{x = 2} [/tex]
Now, let's find the final mass (m) of this isotope after the elapsed time, let's see:
[tex] m = \dfrac{m_o}{2^x} [/tex]
[tex] m = \dfrac{10}{2^{2}} [/tex]
[tex] m = \dfrac{10}{4} [/tex]
[tex] \boxed{\boxed{m = 2.5\:g}}\end{array}}\qquad\checkmark [/tex]
I Hope this helps, greetings ... DexteR! =)
