Structure Of Atom Ques 17
17. In hydrogen atom, the de-Broglie wavelength of an electron in the second Bohr orbit is [Given that Bohr radius, $a_0=52.9 $ $\mathrm{pm}$ ]
[NEET Odisha 2019]
(a) $105.8 $ $\mathrm{pm}$
(b) $211.6 $ $\mathrm{pm}$
(c) $211.6 $ $\pi $ $\mathrm{pm}$
(d) $52.9$ $ \pi $ $\mathrm{pm}$
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Answer:
Correct Answer: 17.(c)
Solution: (c)
$ \begin{aligned} n \lambda & =2 \pi r \\ \lambda & =\frac{2 \pi}{n} \mathrm{r} \\ r_n & =\mathrm{a}_0 n^2 \\ r_2 & =52.9 \times(2)^2 \mathrm{pm} \\ \therefore \quad \lambda \quad \lambda & =\frac{2 \pi}{2} \times 52.9 \times 4 \\ \lambda & =211.6 \pi \mathrm{pm} \end{aligned} $
BETA
