Answer
$3.025\times10^{5}$
Work Step by Step
The active medium in a particular laser that generates laser light at a wavelength of $\lambda=694\;nm$ is $L=6.00\;cm$ long and $d=1.00\;cm$ in diameter.
We treat the medium as an optical resonance cavity analogous to a closed organ pipe.
For closed organ pipe, the general formula wavelengths is
$\lambda=\frac{4L\mu}{2n-1}$
where, $n=1,2,3,4................$. The value of $n$ also corresponds to the number of nodes. $\mu$ is the refractive index of the material.
Substituting the given values, we obtain
$694\times10^{-7}=\frac{4\times6\times1.75}{2n-1}$
or, $2n-1=6.05\times10^{5}$
or, $n=3.025\times10^{5}$
Therefore, the number of standing-wave nodes are along the laser axis is $3.025\times10^{5}$
