Question

According to Bohr's theory, $E_n=$ Total energy, $K_n=$ Kinetic energy, $V_n=$ Potential energy, $R_n=$ Radius of nth orbit. Match Column I with Column II:

Column I		Column II
A	$\frac{V_n}{K_n}=?$	P	0
B	If radius of nth orbit $\propto E_n^x,x=?$	Q	-1
C	Angular momentum in lowest orbital	R	-2
D	$\frac{1}{r^n}\alpha Z^y,y=?$	S	1

• A. $(A)\to (P);(B)\to (Q);(C)\to (R);(D)\to (S)$
• B. $(A)\to (R);(B)\to (Q);(C)\to (P);(D)\to (S)$
• C. $(A)\to (Q);(B)\to (R);(C)\to (P);(D)\to (S)$
• D. $(A)\to (S);(B)\to (Q);(C)\to (P);(D)\to (R)$

Answer 1

Answer: (B)

(A) Potential energy $=-Z{e}^2/r$
Kinetic energy $=Z{e}^2/2r$
Therefore,
$\frac{V_n}{K_n}=-2$
(B) Total energy $=-Z{e}^2/2r$.
Therefore, $r_n\propto E-1$; Hence, $x=-1$.
(C) Angular momentum $=nh/2\pi$.
For $n=0$, angular momentum is zero.
(D) $r_n=a_o{n}^2/Z$.
Therefore, $r_n\propto Z^{-1}$
or $1/r_n\propto Z;$ Hence, $y=1$.