Question

The radius of $1st$ orbit of $H$ is $y\mathring{A}$, then De-Broglie wavelength in the $4th$ orbit of $H{e}^{+}$ is given by:

• A. $2\pi y\mathring{A}$
• B. $4\pi y\mathring{A}$
• C. $6\pi y\mathring{A}$
• D. $8\pi y\mathring{A}$

Answer 1

Answer: (B)

$4\pi y\mathring{A}$

$r_n=r_1{n}^2/z$

for $H{e}^{+}$ fourth orbit

$r_4=r_1\times 4^2/2=8r_1=8y$

We know $mvr=nh/2\pi$

substituting values

$mv8y=4h/2\pi$

$h/mv=4\pi y=\lambda$