Question

If the radius of first Bohr orbit of hydrogen atom is '$x$' then de Broglie wavelength of electron in $3$rd orbit is nearly:

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

Answer 1

Answer: (B)

$6\pi x$

$r_n=$radius of $n_{t}h$ orbit and $r_3=$radius of $3rd$ orbit

$\lambda =$wavelength

$r_n=n^2{r}_1$ and $r_3=9r_1=9x$

$mv9x=3$$\frac{h}{2\pi }$

$\frac{h}{mv}=6\pi x$

So, $\lambda =6\pi x$