MCQ
An electron is moving in Bohr's fourth orbit. Its de $-$ Broglie wavelength is $2$. Calculate the circumference of the fourth orbit.
- A$2\lambda$
- ✓$4\lambda$
- C$\frac{4}{\lambda}$
- D$\frac{2}{\lambda}$
✓
Answer
Correct option: B.
$4\lambda$
According to Bohr's concept,
$\therefore\text{mvr}=\frac{\text{nh}}{2\pi}\Big(\because\lambda=\frac{\text{h}}{\text{mv}}\Big)$ and $\text{n}=4$
$\therefore$ Circumference $=2\pi\text{r}=4.\frac{\text{h}}{\text{mv}}=4\lambda$
$\therefore\text{mvr}=\frac{\text{nh}}{2\pi}\Big(\because\lambda=\frac{\text{h}}{\text{mv}}\Big)$ and $\text{n}=4$
$\therefore$ Circumference $=2\pi\text{r}=4.\frac{\text{h}}{\text{mv}}=4\lambda$
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