The half-life is the time the sample takes to reduce to half of its original value. If we call [tex]m_0[/tex] the initial mass of the sample, this means that after 1 half-life the mass will be [tex] \frac{m_0}{2} [/tex], after 2 half-lives the mass will be [tex] \frac{m_0}{4} [/tex], and so on..
Therefore, after x half-lives the mass of the sample will be
[tex]m= \frac{m_0}{2^x}[/tex] (1)
In our problem, the initial mass is [tex]m_0 = 2000 g[/tex] while the mass after x half-lives is [tex]m=125 g[/tex], so by using equation (1) we can find the value of x:
[tex]2^x = \frac{m_0}{m}= \frac{2000 g}{125 g}=16 [/tex]
From which
[tex]x=4[/tex]
And the correct answer is C).
