Question

If the radius of first Bohr orbit of H 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. $x/3$

Answer 1

Answer: (B)

$6\pi x$

According to Bohr's postulate,

$m{v}_n{r}_n=nh/2\pi \left(n^{th}orbit\right)$

radius of nth orbit, $r_n=n^2.r_1$

given that $r_1=x$

thus in third orbit: $m.v_3.r_3=3h/2\pi$

Debroglie wavelength in 3rd orbit is given by:

$\lambda =h/m_3{v}_3$

thus $\lambda =2\pi .r_3/3$

or $\lambda =2\pi {.3}^{2}x/3$

$\lambda =6\pi x$

Thus If the radius of the first Bohr orbit of H atom is x, then de Broglie wavelength of an electron in 3rd orbit is nearly $6\pi x$

So, option $B$ is correct.