Chất \(_{90}^{232}\textrm{Th}\) là chất phóng xạ...

D

- Hướng dẫn giải

Ta có: 
\(_{90}^{232}\textrm{Th}\rightarrow _{82}^{208}\textrm{Pb}+x_{2}^{4}\textrm{He}+y_{-1}^{0}\textrm{e}\)
Ta có:
\(\left\{\begin{matrix} 232=208+4x+0y\\90=82+2x-y \end{matrix}\right.\Rightarrow \left\{\begin{matrix} x=6\\y=4 \end{matrix}\right.\)
Cứ 1 hạt Th thì có 6 hạt \(\alpha\).
Sau 3T: \(\left\{\begin{matrix} N_{\alpha }=6.\Delta N_{Th}=6.N_{0}(1-2^{\frac{-t}{T}})\\ N_{Th}=N_{0}.2^{\frac{-t}{T}} \end{matrix}\right.\)
\(\Rightarrow \frac{N_{\alpha }}{N_{Th}}=\frac{6.N_{0}(1-2^{\frac{-t}{T}})}{N_{0}.2^{\frac{-t}{T}}}=6(2^{\frac{t}{T}}-1)\)
\(=6.(2^{3}-1)=42\)
\(\Rightarrow\) Chọn câu D.