MCQ
In an atom two electrons move around the nucleus in circular orbits of radii $R$ $\&$ $4R.$ The ratio of the time taken by them to complete one revolution is :
- A$1 : 4$
- B$4 : 1$
- ✓$1 : 8$
- D$8 : 7$
✓
Answer
Correct option: C.
$1 : 8$
c
If the electron is moving with a velocity v around the nucleus the time taken by it to
If the electron is moving with a velocity v around the nucleus the time taken by it to
complete one revolution would be given by $T=2 \pi r / v$
Now from Bohr's theory we have
$\operatorname{r} \alpha \mathrm{n}^{2}$ and $\mathrm{v} \propto \frac{1}{\mathrm{n}}$
Hence $\mathrm{T} \propto \mathrm{n}^{3} \mathrm{T}^{2} \propto \mathrm{n}^{6}$ or $\mathrm{T}^{2} \propto \mathrm{r}^{3}$
Hence we write
$\left(\frac{T_{1}}{T_{2}}\right)^{2}=\left(\frac{R}{4 R}\right)^{3}=\frac{1}{64}$ or $\frac{T_{1}}{T_{2}}=\frac{1}{8}$
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