The question is incomplete, here is the complete question:
Recall that m(t) = m.(1/2)^t/h for radioactive decay, where h is the half-life. Suppose that a 500 g sample of phosphorus-32 decays to 356 g over 7 days. Calculate the half life of the sample.
<u>Answer:</u> The half life of the sample of phosphorus-32 is ![14.28days^{-1}](https://tex.z-dn.net/?f=14.28days%5E%7B-1%7D)
<u>Step-by-step explanation:</u>
The equation used to calculate the half life of the sample is given as:
![m(t)=m_o(1/2)^{t/h}](https://tex.z-dn.net/?f=m%28t%29%3Dm_o%281%2F2%29%5E%7Bt%2Fh%7D)
where,
m(t) = amount of sample after time 't' = 356 g
= initial amount of the sample = 500 g
t = time period = 7 days
h = half life of the sample = ?
Putting values in above equation, we get:
![356=500\times (\frac{1}{2})^{7/h}\\\\h=14.28days^{-1}](https://tex.z-dn.net/?f=356%3D500%5Ctimes%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B7%2Fh%7D%5C%5C%5C%5Ch%3D14.28days%5E%7B-1%7D)
Hence, the half life of the sample of phosphorus-32 is ![14.28days^{-1}](https://tex.z-dn.net/?f=14.28days%5E%7B-1%7D)