Question

Match the items in column I with their respective values in column II.
1. According to Bohr's thoery
$E_n$ = Total energy
$K_n$ = Kinetic energy
$V_n$ = Potential energy
$r_n$ = Radius of nth orbit energy

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ a.\frac{V_n}{K_n}=?& p.0\\ b.\text{If radius of}{n}^{th}\text{orbit}\propto E_n^x,x=?& q.-1\\ c.\text{Angular momentum in lowest orbital}& r.-2\\ d.\frac{1}{r_n}\propto Z^y,y=?& s.1\end{array}$

• A. a > r, b > p, c > q, d > s
• B. a > r, b > q, c > p, d > s
• C. a > s, b > q, c > p, d > r
• D. a > p, b > q, c > s, d > r

Answer 1

The correct option is B

a > r, b > q, c > p, d > s

(a $\to$ r) For Bohr's electron in H atom
KE = $\frac{e^2}{2r}$
PE = $\frac{-e^2}{r}$
$\frac{V_n}{K_n}=\frac{PE}{KE}=2$

(b $\to$ q) r $\propto n^2$
$E_n\propto \frac{1}{n^2}$
or $n^2\propto \frac{1}{E_n}$
or $r\propto \frac{1}{E_n}$
or $r\propto E_n^{-1}$

(c $\to$ p) The orbital angular momentum is: $\frac{h}{2\pi }\sqrt{l(l+1)}$
The orbital angular momentum for an electron in s orbital (l = 0) (lowest orbital is 1s) is 0.

$(d\to s)r\propto \frac{1}{Z}$
or $\frac{1}{r}\propto Z$