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Câu hỏi: Theo mẫu nguyên tử Bo trong nguyên tử Hydro. Tỉ số giữa tốc độ của êlectron trên quỹ đạo K và tốc độ của êlectron trên quỹ đạo M bằng
A. 1
B. 3
C. 4
D. 9
A. 1
B. 3
C. 4
D. 9
+ Ở trạng thái dừng thứ n:$-\left\{ \begin{aligned}
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{r}_{\text{k}}^{\text{2}}}\text{= }{{\text{m}}_{\text{e}}}\dfrac{\text{v}_{\text{k}}^{\text{2}}}{{{\text{r}}^{\text{2}}}} \\
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{r}_{\text{M}}^{\text{2}}}\text{= }{{\text{m}}_{\text{e}}}\dfrac{\text{r}_{\text{M}}^{\text{2}}}{{{\text{r}}_{\text{M}}}} \\
\end{aligned} \right\}(*)$
Mà ${{\text{r}}_{\text{n}}}\text{= nr}_{\text{0}}^{\text{2}}$, với ${{\text{r}}_{\text{k}}}\text{= }{{\text{r}}_{0}}$, ${{\text{r}}_{\text{M}}}\text{= }{{\text{r}}_{\text{3}}}$ nên $\Rightarrow \left\{ \begin{aligned}
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{r}_{0}^{\text{2}}}\text{= }\dfrac{\text{mv}_{0}^{\text{2}}}{{{\text{r}}_{0}}} \\
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{81r}_{0}^{\text{2}}}\text{= }{{\text{m}}_{\text{e}}}\dfrac{\text{r}_{\text{M}}^{\text{2}}}{\text{9}{{\text{r}}_{0}}} \\
\end{aligned} \right\}\Rightarrow \dfrac{{{\text{v}}_{\text{0}}}}{{{\text{v}}_{\text{3}}}}=3$
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{r}_{\text{k}}^{\text{2}}}\text{= }{{\text{m}}_{\text{e}}}\dfrac{\text{v}_{\text{k}}^{\text{2}}}{{{\text{r}}^{\text{2}}}} \\
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{r}_{\text{M}}^{\text{2}}}\text{= }{{\text{m}}_{\text{e}}}\dfrac{\text{r}_{\text{M}}^{\text{2}}}{{{\text{r}}_{\text{M}}}} \\
\end{aligned} \right\}(*)$
Mà ${{\text{r}}_{\text{n}}}\text{= nr}_{\text{0}}^{\text{2}}$, với ${{\text{r}}_{\text{k}}}\text{= }{{\text{r}}_{0}}$, ${{\text{r}}_{\text{M}}}\text{= }{{\text{r}}_{\text{3}}}$ nên $\Rightarrow \left\{ \begin{aligned}
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{r}_{0}^{\text{2}}}\text{= }\dfrac{\text{mv}_{0}^{\text{2}}}{{{\text{r}}_{0}}} \\
& \text{k}\dfrac{{{\text{e}}^{\text{2}}}}{\text{81r}_{0}^{\text{2}}}\text{= }{{\text{m}}_{\text{e}}}\dfrac{\text{r}_{\text{M}}^{\text{2}}}{\text{9}{{\text{r}}_{0}}} \\
\end{aligned} \right\}\Rightarrow \dfrac{{{\text{v}}_{\text{0}}}}{{{\text{v}}_{\text{3}}}}=3$
Đáp án B.