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  4. If the radius of first Bohr orbit is x, then de Broglie wavelength of electron in 3rd orbit is nearly.

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Q. If the radius of first Bohr orbit is $x$, then de Broglie wavelength of electron in $3^{rd}$ orbit is nearly.

Structure of Atom

Solution:

$r_{n} =\frac{n^{2}a_{o}}{Z}, \therefore r_{o} \propto n_{2} $
$\frac{r_{3}}{r_{1}}=\frac{9}{1}$
$ r_{3}=9r_{1}=9x$
Also $mvr_{n} =\frac{nh}{2\pi}$
$mvr_{3} =\frac{3h}{2\pi} $
$mv=\frac{h}{6\pi x}$
$\lambda =\frac{h}{mv}=6\pi x$