Question

According to Bohr theory:
$E_n=$ Total energy
$K_n=$ Kinetic energy
$V_n=$ Potential energy
$r_n=$ Radius of $n$th orbit
Match the following:

Answer 1

$E_n=Totalenergy\to E_n\propto \frac{z^2}{n^2}$

$K_n=Totalenergy\to k_n\propto \frac{z^2}{n^2}$

$V_n=Totalenergy\to V_n\propto \frac{z}{n}$

${\gamma }_n$ =radius of $n^{th}orbit\to r_n\propto \frac{n^2}{z}$

$\frac{V_n}{K_n}\Rightarrow$ $V_n\propto \frac{z}{n}$,$K_n\propto v^2\propto \frac{z^2}{n^2}$

$\frac{V_n}{K_n}\propto \frac{n}{z}$

${\gamma }_n\propto \frac{n^2}{z}$ ,$E_n\propto \frac{z^2}{n^2}$

Put z=1

then $r_n\propto E_n^{-1}$

$x=-1$

$\left(C\right)$ Angular momentum is lowest orbital $\Rightarrow n=1,l=0\Rightarrow$Zero angular momentum

$mvr=\frac{nh}{2\pi }$

$\left(D\right)$ $\frac{1}{{\gamma }^n}\propto z^y$

${\gamma }_n\propto \frac{z^2}{z}$

$\frac{1}{{\gamma }_n}\propto \frac{z}{n^2}$

$\Rightarrow y=1$