Question

Number of waves made by the pion when orbiting in third excitation state are:

• A. $3$
• B. $4$
• C. $3Z^2$
• D. $4Z^2$

Answer 1

The correct option is B $4$

The number of waves made by pion can be calculated as:

$N=\frac{2\pi r}{\lambda }$, where $r$ is the radius of orbit and $\lambda$ is the wavelength

Acording to De-Broglie, $\lambda =\frac{h}{m_{\pi }v}$, where $v=\frac{nh}{2\pi m_{\pi }r}$ according to quantization of angular momentum

therefore, $N=\frac{2\pi r{m}_{\pi }}{h}\times \frac{nh}{2\pi m_{\pi }r}=n$, where n is principle quantum number.

therefore, in third excited state number of waves made by pion will be $N=4$.