Thorium-234 ($^{234}_{90}\text{Th}$) is radioactive. It undergoes decay by $\beta$-emission to produce an isotope of protactinium (Pa).
(a)[2]
Complete the nuclide equation for this decay: $^{234}_{90}\text{Th} \rightarrow \\dots\dots\text{Pa} + \\dots\beta$.
(b)[3]
Calculate the count rate for the $\beta$-particle emission from the thorium in the sample once $72\text{ days}$ have elapsed.
(c)[3]
State and explain how this would change the observed count rate for the sample in (b) after $72\text{ days}$.
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