Question

In H-atom, if ‘x’ is the radius of first Bohr orbit, de Broglie wavelength of an electron in $3^{rd}$ orbit is:

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

Answer 1

The correct option is B

$6\pi x$

$r_n=\frac{0529\times n^2}{Z}{A}^{\circ }$

$r_1=\frac{0.529\times (1{)}^2}{\left(1\right)}=x$

$r_3=\frac{0.529\times (3{)}^2}{\left(1\right)}=\frac{0.529\times 9}{1}=9x$

We know that,

$2\pi r=n\lambda 2\pi 9x=\left(3\right)\lambda \lambda =6\pi x$