Particle in a Box - Physical Chemistry - Chemistry Previous Year Questions

1

2008 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2008

A particle is confined to a one-dimensional box of length 1 mm. If the length is changed by 10^-9 m, the % change in the ground state energy is

A

2 x 10^-4

B

2 x 10^-7

C

2 x 10^-2

D

0

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2

2009 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2009

The lowest allowed energy is equal to zero for

A

the hydrogen atom

B

a rigid rotor

C

a harmonic oscillator

D

a particle in a 3-dimensional box

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3

2009 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2009

The degeneracy of a quantum particle in a cubic box having energy four times that of the lowest energy is

A

3

B

6

C

1

D

4

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4

2011 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2011

The wave function for a quantum mechanical particle in a 1-dimensional box of length 'a' is given by \(\psi = A \sin \frac{\pi x}{a}\). The value of 'A' for a box of length 200 nm is

A

\(4\times10^4\ (\text{nm})^2\)

B

\(10\sqrt{2}\ (\text{nm})^{-1/2}\)

C

\(\sqrt{2}/10\ (\text{nm})^{-1/2}\)

D

\(0.1\ (\text{nm})^{-1/2}\)

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5

2013 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2013

Two trial wave functions $\psi_1 = c_1 x(a-x)$ and $\psi_2 = c_2 x(a-x) + c_3 x^2 (a-x)^2$ give ground state energies $E_1$ and $E_2$, respectively, for the microscopic particle in a 1-D boxy using the variation method. If the exact ground state energy is $E_0$, the correct relationship between $E_0$, $E_1$ and $E_2$ is

A

E_0 = E_1 = E_2

B

E_0 < E_1 < E_2

C

E_0 < E_2 < E_1

D

E_0 > E_2 = E_1

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6

2016 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2016

The linear momentum of a particle described by the wavefunction e^-ikx is

A

kħ

B

-kħ

C

kħi

D

-kħi

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7

2019 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2019

Suppose the wave function of a one dimensional system is
\[ \psi = \sin(kx)\exp(3ikx) \]
In an experiment measuring the momentum of the system, one of the expected outcomes is

A

0

B

ħk

C

2 ħk

D

3 ħk

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8

2019 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2019

A particle in one dimensional box of length 2a with potential energy
V = { 0 |x| < a ; ∞ |x| > a }
is perturbed by the potential V' = cx eV, where c is a constant. The 1^st order correction to the 1^st excited state of the system is ______ × c eV.

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9

2024 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2024

The wave function of a particle in a cubic box (of side \( L \)) is given by \( \psi(x, y, z) = \sqrt{32/L^3} \sin\frac{\pi x}{L} \cos\frac{\pi x}{L} \sin\frac{2\pi y}{L} \sin\frac{\pi z}{L} \).
The ratio of the energy of the state corresponding to the above wave function to the ground state energy is ____.
(rounded off to the nearest integer)

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10

2025 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2025

Consider two non-interacting particles confined to a one-dimensional box with infinite potential barriers. Their wavefunctions are ψ₁ and ψ₂ and energies are E₁ and E₂, respectively. The INCORRECT statement(s) about this system is/are

A

The total energy is E₁ + E₂

B

The total wavefunction is ψ₁ + ψ₂

C

The total energy is E₁E₂

D

The total wavefunction is ψ₁ψ₂

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11

2025 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2025

Wavefunctions and energies for a particle confined in a cubic box are \(\psi_{n_x,n_y,n_z}\) and \(E_{n_x,n_y,n_z}\), respectively. The functions \(\phi_1\), \(\phi_2\), \(\phi_3\), and \(\phi_4\) are written as linear combinations of \(\psi_{n_x,n_y,n_z}\). Among these functions, the eigenfunction(s) of the Hamiltonian operator for this particle is/are

A

\(\phi_2\)

B

\(\phi_4\)

C

\(\phi_3\)

D

\(\phi_1\)

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12

2007 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2007

Consider a particle of mass m moving in a one-dimensional box under the potential V=0 for 0 ≤ x ≤ a and V = ∞ outside the box. When the particle is in its lowest energy state the average momentum ⟨p_x⟩ of the particle is

A

0

B

h/a

C

h/(2a)

D

h/(2πa)

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13

2007 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2007

The uncertainty in the momentum (Δp_x) of the particle in its lowest energy state is

A

0

B

h/a

C

h/(2a)

D

h/(2πa)

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14

2010 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2010

For eigen functions ψ₁ = √(2/b) sin(πx/b) and ψ₂ = √(2/b) sin(2πx/b) of particle in a 1-D box of length b (0 ≤ x ≤ b)

A

ψ₁ is normalized and orthogonal to ψ₂

B

ψ₁ is normalized but not orthogonal to ψ₂

C

ψ₂ is normalized and orthogonal to ψ₁

D

ψ₂ is neither normalized nor orthogonal to ψ₁

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15

2010 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2010

An electron of mass 'm' is confined to a one dimensional box of length 'b'. If it makes a radiative transition from second excited state to the ground state, the frequency of the photon emitted is

A

\(\frac{9h}{8mb^2}\)

B

\(\frac{3h}{8mb^2}\)

C

\(\frac{h}{mb^2}\)

D

\(\frac{2h}{mb^2}\)

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16

2015 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2015

The difference in the ground state energies (kJ/mol) of an electron in one-dimensional boxes of lengths 0.2 nm and 2 nm is ____________________

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17

2017 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2017

The wavelength associated with a particle in one-dimensional box of length L is (n refers to the quantum number)

A

2L/n

B

L/n

C

nL

D

L/2n

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18

2017 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2017

Assume 1,3,5-hexatriene to be a linear molecule and model the π electrons as particles in a one-dimensional box of length 0.70 nm. The wavelength (in nm) corresponding to the transition from the ground-state to the first excited-state is ________________________

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19

2018 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2018

The π electrons in benzene can be modelled as particles in a ring that follow Pauli's exclusion principle. Given that the radius of benzene is 1.4 Å, the longest wavelength of light that is absorbed during an electronic transition in benzene is __________ nm. (Up to one decimal place. Use m_e = 9.1×10^-31 kg, h = 6.6×10^-34 J s, c = 3.0×10⁸ m s^-1)

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20

2020 · Chemistry · Physical Chemistry · Particle in a Box

Chemistry (CY) 2020

The % error (rounded off to two decimal places) in the ground state energy of a particle in a one dimensional box of length 'a' described by a trial variation function φ = x(a−x), where 0 ≤ x ≤ a, is ______
(Given: The true ground state energy of the above system is h$^2$/8ma$^2$; ∫$_0^a$ φ*dφ dτ = a$^5$/30)

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