Question

An electron is moving in Bohr's third orbit. Its de Broglie wavelength is $\lambda$. Then the circumference of the third orbit?

• A. $\lambda$
• B. $2\lambda$
• C. $3\lambda$
• D. $4\lambda$

Answer 1

The correct option is C $3\lambda$

De-broglie wavelength is given by:

${\lambda }_n=h/m_n{v}_n$

According to Bohr's postulate

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

on rearranging we get:

$h/m_n{v}_n=2\pi r_n/n$

thus ${\lambda }_n=2\pi r_n/n$

circumference of $n^{th}$ orbit =$2\pi r_n$

therefore ${\lambda }_n=circumference/n$

or $circumference=n.{\lambda }_n$

given that ${\lambda }_3=\lambda$

thus circumference of 3rd orbit is (n=3)

$circumference=3.{\lambda }_3=3\lambda$