Question

De-Broglie wavelength of $e^{-}$ in third Bohr orbit of hydrogen atom is

• A. $3\stackrel{\circ }{A}$
• B. $5\stackrel{\circ }{A}$
• C. $10\stackrel{\circ }{A}$
• D. $2\stackrel{\circ }{A}$

Answer 1

The correct option is C $10\stackrel{\circ }{A}$

Radius of $n^{th}$ orbit is given by
$r_n=n^{2}R$
where $R$ is radius of first orbit of hydrogen atom.$(R=0.53\stackrel{\circ }{A})$

Using $2\pi r_n=n\lambda$
$2\pi r_n=3\lambda$
$\lambda =\frac{2\pi r_n}{3}=\frac{2\pi n^{2}R}{3}$
$\lambda =\frac{2\pi }{3}\times 0.53\times \frac{9}{1}$
$\lambda =6\pi \times 0.53$
$=10\stackrel{\circ }{A}$