Question

Wavelength of the de-Broglie wave of an electron revolving in the sixth orbit of the hydrogen atom is: $(r_0$is the Bohr's radius = 0.529 $\mathring{A}$)

• A. $\pi r_0$
• B. $12\pi r_0$
• C. $6\pi r_0$
• D. $4\pi r_0$

Answer 1

The correct option is B $12\pi r_0$

Angular momentum of an electron ($mvr$) is an integral multiple of $\frac{h}{2\pi }$
Thus $mvr=\frac{6h}{2\pi }$ for 6th orbit......(1)
$\lambda =\frac{h}{mv}$......(2)
From (1) and (2)
$\lambda =\frac{2\pi r}{6}$......(3)
But the radius of sixth orbit $r=r_0{n}^2=r_0(6{)}^2$.......(4)
From (3) and (4)
$\lambda =12\pi r_0$