Question 428: Atoms & Nuclei

Question

If the radius of the first Bohr orbit is '$$r$$' then the de-Broglie wavelength of the electron in the $$4^{	ext {th }}$$ orbit will be

Accepted Answer

According to Bohr's second postulate,
$$\frac{\mathrm{nh}}{2 \pi}=\mathrm{mvr}_{\mathrm{n}}$$
$$	herefore$$ de-Broglie wavelength, $$\lambda_n=\frac{h}{m v}=\frac{2 \pi r_n}{n}$$
Also, $$\mathrm{r}_{\mathrm{n}} \propto \mathrm{n}^2$$
$$	herefore \quad$$ The de-Broglie wavelength of the electron in the $$4^{	ext {th }}$$ orbit is:
$$\begin{aligned}
&\lambda_4=\frac{2 \pi r_4}{4}=\frac{2 \pi 	imes(16 r)}{4} \
&	herefore \quad \lambda_4 =8 \pi r
\end{aligned}$$

Answer

$$4 \pi \mathrm{r}$$

Answer

$$6 \pi \mathrm{r}$$

Answer

$$8 \pi \mathrm{r}$$

Answer

$$\frac{\pi r}{4}$$

Atoms & Nuclei

If the radius of the first Bohr orbit is '$r' then the de-Broglie wavelength of the electron in the 4^{\text {th }}$ orbit will be

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