According to Bohr's theory En= total energy, Kn= kinetic energy, Vn= potential energy, rn= radius of n mathrmth orbit. Match the items of column I with values of column II Column I Column II A Vn/Kn = ? P 0 B If radius of nth orbit propto Exn, x = ? Q -1 C Angular momentum in lowest orbital R -2 D (1/rn) propto Zy , y = ? S 1

Question

According to Bohr's theory En= total energy, Kn= kinetic energy, Vn= potential energy, rn= radius of n mathrmth orbit. Match the items of column I with values of column II Column I Column II A Vn/Kn = ? P 0 B If radius of nth orbit propto Exn, x = ? Q -1 C Angular momentum in lowest orbital R -2 D (1/rn) propto Zy , y = ? S 1 (A) (A arrow Q) (Barrow S)(Carrow P)(D arrow S) (B) (A arrow R) (Barrow Q)(Carrow P)(D arrow S) (C) (A arrow P) (Barrow S)(Carrow Q)(D arrow R) (D) (A arrow P) (Barrow R)(Carrow S)(D arrow Q)

Tardigrade Admin · Accepted Answer

According to Bohr's theory
Potential energy

(V_{n}) = - \frac{1}{4 π ε _{0}} \frac{Z e ^{2}}{r};

Kinetic energy

(K_{n}) = \frac{1}{8 π ε _{0}} \frac{Z e ^{2}}{r}

Radius of

n^{th}

orbit

(r_{n}) = \frac{n ^{2} h ^{2} ε _{0}}{πm Z e ^{2}}

Potential energy

(E_{n}) = - \frac{m e ^{4}}{8 ε _{0}^{2} h ^{2}} (\frac{1}{n ^{2}})

\frac{V _{n}}{K _{n}} = \frac{- \frac{1}{4 π ε _{0}} \frac{Z e ^{2}}{r}}{\frac{1}{8 π ε _{0}} \frac{Z e ^{2}}{r}} = - 2 (A \to R)

E_{n} \propto \frac{1}{n ^{2}} \propto \frac{1}{r _{n}}

r^{n} \to E_{n}^{x} ∴ x = - 1. (B \to Q)

l

, the orbital quantum number, is connected to the total
angular momentum of the electron. This quantum number is an integer less than

n

, and the total angular momentum of the electron can be calculated using:
Total angular momentum,

L = [l (l + 1)]^{1/2} \frac{h}{2 π} (l = 0, 1, 2, \dots, n - 1)

The lowest energy orbital in the hydrogen atom is the

1 s

orbital, which corresponds with

n = 1, l = 0

and

m = 0

.
Hence total angular moment in lowest orbital

= 0

.

(C \to P)

\frac{1}{r ^{n}} \propto Z^{y}

as

r_{n} \propto \frac{1}{Z}

∴ y = 1 (D \to S)

$(A \to Q) (B \to S) (C \to P) (D \to S)$

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

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

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

Column I		Column II
A	$V_{n} / K_{n} =$ ?	P	0
B	If radius of $n^{t h}$ orbit $\propto E_{n}^{x}, x =$ ?	Q	-1
C	Angular momentum in lowest orbital	R	-2
D	$\frac{1}{r _{n}} \propto Z^{y}, y =$ ?	S	1

(A→Q)(B→S)(C→P)(D→S)

(A→R)(B→Q)(C→P)(D→S)

(A→P)(B→S)(C→Q)(D→R)

(A→P)(B→R)(C→S)(D→Q)

$(A \to Q) (B \to S) (C \to P) (D \to S)$

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

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

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