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

Answer 1

Answer: (B)

(A) Potential energy $=-Z e^{2} / r$
Kinetic energy $=Z e^{2} / 2 r$
Therefore,
$\frac{V_{n}}{K_{n}}=-2$
(B) Total energy $=-Z e^{2} / 2 r$.
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, $y=1$.