Question

In a H atom, if 'x' is the radius of the first Bohr orbit, the de Broglie wavelength of an electron in the third Bohr orbit is

• A. $3\pi x$
• B. $6\pi x$
• C. $9x^2$
• D. $\frac{x^2}{2}$

Answer 1

The correct option is B $6\pi x$

The radius of the first Bohr orbit of the H atom is $0.529\stackrel{o}{A}$
Therefore, $x=0.529\stackrel{o}{A}$
$r_n=\frac{0.529\times n^2}{z}\stackrel{o}{A}$
where, n= number of orbits
So, if $r_1=x,then{r}_3=3^{2}x=9x$
And $\lambda$=$\frac{2\pi r}{n}$
$\frac{2\pi \left(9x\right)}{n}=6\pi x$