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According to Bohr's theory $E_n=$ Total energy, $K_n=$ Kinetic energy, $V_n=$ Potential energy, $r_n=$ Radius of $n$th orbit

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The correct answer is:
(A) R, (B) Q, (C) P, (D) S
(A) R, (B) Q, (C) P, (D) S
According to Bohr's theory,
Total energy is $E_n=K_n+V_n$
Kinetic energy $=K_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$
Potential energy $=V_n=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$
$\therefore \quad E_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$
Radius of $n$th orbit $\left(r_n\right)=\frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2}$ $$ E_n=-\frac{m e^4}{8 \varepsilon_0^2 h^2} \times \frac{1}{n^2} $$ (A) $\frac{V_n}{K_n}=\frac{-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}{\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}=-2$
Hence, $(A)$ match with $(R)$.
(B) $E_n \propto \frac{1}{n^2}$ or $E_n \propto \frac{1}{r_n}$
Radius of $n$th orbit $r_n \propto E_n^x$ $\therefore \quad x=-1$
Hence, (B) match with (Q).
(C) Angular momentum $=\frac{h}{2 \pi} \sqrt{l(l+1) l}=0,1,2, \ldots$
For the lower orbit $n=1$
$\therefore \quad l=0$ and $m=0$
Hence, angular momentum of lowest orbit $=\frac{h}{2 \pi} \sqrt{0(0 H)}=0$
(C) match with (P)
(D) $\frac{1}{r^n} \propto Z^y$ as $r_n \propto \frac{1}{Z} \therefore y=1$
Hence, (D) match with (S).
Total energy is $E_n=K_n+V_n$
Kinetic energy $=K_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$
Potential energy $=V_n=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$
$\therefore \quad E_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$
Radius of $n$th orbit $\left(r_n\right)=\frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2}$ $$ E_n=-\frac{m e^4}{8 \varepsilon_0^2 h^2} \times \frac{1}{n^2} $$ (A) $\frac{V_n}{K_n}=\frac{-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}{\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}=-2$
Hence, $(A)$ match with $(R)$.
(B) $E_n \propto \frac{1}{n^2}$ or $E_n \propto \frac{1}{r_n}$
Radius of $n$th orbit $r_n \propto E_n^x$ $\therefore \quad x=-1$
Hence, (B) match with (Q).
(C) Angular momentum $=\frac{h}{2 \pi} \sqrt{l(l+1) l}=0,1,2, \ldots$
For the lower orbit $n=1$
$\therefore \quad l=0$ and $m=0$
Hence, angular momentum of lowest orbit $=\frac{h}{2 \pi} \sqrt{0(0 H)}=0$
(C) match with (P)
(D) $\frac{1}{r^n} \propto Z^y$ as $r_n \propto \frac{1}{Z} \therefore y=1$
Hence, (D) match with (S).
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