Answer the following by appropriately matching the lists based on the information given in the paragraph Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\text{th}}$ orbit of the atom and List-II contains options showing how they depend on $n$. List-I (I) Radius of the $n^{\text{th}}$ orbit (II) Angular momentum of the electron in the $n^{\text{th}}$ orbit (III) Kinetic energy of the electron in the $n^{\text{th}}$ orbit (IV) Potential energy of the electron in the $n^{\text{th}}$ orbit List-II (P) $\propto \mathrm{n}^{-2}$ (Q) $\propto \mathrm{n}^{-1}$ (R) $\propto \mathrm{n}^{0}$ (S) $\propto \mathrm{n}^{1}$ (T) $\propto \mathrm{n}^{2}$ (U) $\propto \mathrm{n}^{1/2}$ Which of the following options has the correct combination considering List-I and List-II?

JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Atomic Structure

Answer the following by appropriately matching the lists based on the information given in the paragraph

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the

n^{th}

orbit of the atom and List-II contains options showing how they depend on

n

.

List-I
(I) Radius of the

n^{th}

orbit
(II) Angular momentum of the electron in the

n^{th}

orbit
(III) Kinetic energy of the electron in the

n^{th}

orbit
(IV) Potential energy of the electron in the

n^{th}

orbit

List-II
(P)

\propto n^{- 2}

(Q)

\propto n^{- 1}

(R)

\propto n^{0}

(S)

\propto n^{1}

(T)

\propto n^{2}

(U)

\propto n^{1/2}

Which of the following options has the correct combination considering List-I and List-II?

(A)(II), (R)
(B)(I), (P)
(C)(I), (T)✓ Correct
(D)(II), (Q)

Answer: (C)

Solution

For Bohr's model:

Radius: $r = 0.529 \times \frac{n ^{2}}{Z}$ Å → $r \propto n^{2}$ → (I), (T) ✓

Angular momentum: $m v r = \frac{nh}{2 π}$ → $L \propto n$ → (II), (S)

Kinetic energy: $K E = + 13.6 \times \frac{Z ^{2}}{n ^{2}}$ eV → $K E \propto n^{- 2}$ → (III), (P)

Potential energy: $P E = - 2 \times 13.6 \times \frac{Z ^{2}}{n ^{2}}$ eV → $P E \propto n^{- 2}$ → (IV), (P)

Option (C) correctly matches (I) with (T).

JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Single correct option

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JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Atomic Structure

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