Answered: (a) For a particle in the stationary…

(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom

Section: Chapter Questions

Problem 11.61E: What is the physical explanation of the difference between a particle having the 3-D rotational...

See similar textbooks

Related questions

Q: For a particle in the stationary state n of a one dimensional box of length a, find the probability…

Q: Vanadium tetrachloride (VCl4 ) is a bright red colored liquid with a vapor pressure of 5x10-2 torr…

A: The orbital angular momentum of electron inn a given orbital is calculated by using the following…

Q: Construct the potential energy operator of a particle with potential energy V(x)=1/2kfx2, where kf…

A: The information about the location of a particle is given by Born interpretation of the wave…

Q: For a particle in a box of length L and in the state with n = 3, at what positions is the…

A: The wavefunction does not describe exact location of the microscopic particle. It tells about…

Q: Describe what what is meant by the term "uncertainty principle."

A: Chemistry can be defined as the branch of science that deals with composition of substances.

Q: A particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized…

A: Given normalized wave function ψ(x) = a1/2e–ax/2 where 'a' is a constant. Particle freely moving in…

Q: if n=3, what is the maximum allowed value for l?

A: In this question, value of n ( principle quantum number ) is given and you want to determine the…

Q: The moment of inertia of an SF6 molecule is 3.07 × 10−45 kg m2. What is the minimum energy needed to…

A: Given: The moment of interia of an SF6 molecule is 3.07×10-45 kg m2.

Q: Calculate the expectation values of x and x2 for a particle in the state with n = 1 in a…

A: The expectation value of x2 for a particle is given by following expression. The value of ψ for one…

Q: Normalize (to 1) the wavefunction e–ax in the range 0 ≤ x ≤ ∞, with a > 0.

A: Given: The wave function is as follows,

Q: 1. What would be the speed of a proton (mass = 1.673 x 102" g) if it had the same wavelength as a…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a…

A: The expression for the wave function of a particle in a ring is as follows,

Q: the lifetime of the 4p1/2 state of potassium, is 27.3 ns. what are the einstein a and b coefficients…

Q: Calculate the probability of finding the particle in a one-dimensional box of length a in the…

Q: If n = 2, what is the maximum allowed value for ℓ?

A: If n = 2, what is the maximum allowed value for ℓ?

Q: Normalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the…

A: Normalization is the scaling of wave functions so that all the probabilities add to 1.

Q: Functions of the form sin(nπx/L), where n = 1, 2, 3 …, are wavefunctions in a region of length L…

A: The wavefunction is given as,ψ = sin nπxLFor n=1, ψ1 = sin πxLFor n=2, ψ1 = sin 2πxL

Q: 3. Plot the eigenstate and particle probability for a particle in a box, with infinite height walls,…

Q: A possible wavefunction for an electron in a region of length L (i.e. from x=0 to x=L) is 2 πχ. sin…

Q: What is the probability (between 0 and 1) of finding an electron in the 1s state of hydrogen at a…

Q: 4. Given these operators A=d/dx and B=x², can you measure the expectation values of the…

A: We have to use the concept of commutator over here. If the given observable commute with each other,…

Q: The Hamiltonian operator y for the harmonic oscillator is given by Ĥ = - a h? d? + suw? â?, where l…

A: Given: Hamiltonian operator H^=-ℏ22μd2 dx2+12μω2x^2 μ is the reduced mass ω=2πν is the angular…

Q: For the same system as in Exercise E7C.3(a) (Functions of the form sin(nπx/L), where n = 1, 2, 3 …,…

Q: For a particle in a one- dimensional box, the ground state wavefunction is W = ( 2/a)1/2 sin Tx/a…

A: Given Type of box = 1-D box Region range = L4 to 3L4 Probability of finding the particle in a box…

Q: A rotating diatomic molecule absorbs radiation and has moment of inertia, I, equal to 1.00 x 10-46…

Q: For a 1.0 x 10^-26 g particle in a box whose ends are at x=0 and x=2.000 Å, calculate the…

A: A particle confined 1-dimensional box is a fundamental quantum mechanical approximation explaining…

Q: when a sodium atom is deexcited from the first excited state to the ground state, it emits 9 Photon…

Q: Where are the nodes in the wavefunction for a particle confined to a box with 0 < x < a and n=3?

A: Wave function for a particle in a box with 0 < x < a and n=3 No of nodes = to be determined.…

Q: If a nitrogen molecule is trapped in a hypothetical 1-D box of length 1.10 cm, at what value of the…

A: Translational energy :- It is the energy which is associated with displacement of a…

Q: 421) The moment of inertia of an SF, molecule is 3.07 x 10 kg m. What is the minimum energy needed…

A: Given, the moment of inertia of an SF6 molecule = 3.07×10-45 kg m2 The minimum energy needed to…

Q: What are the implica tions of the uncertainty principle?

A: Heisenberg's Uncertainty Principle states that there is inherent uncertainty in the act of measuring…

Q: P7F.9 In this problem you will establish the commutation relations, given in eqn 7E. 14, between the…

Q: For a particle in a two-dimensional square box of length L, if the particle is in the state w2,3 (x,…

A: Wavefunction of a particle in 2D is given by

Q: The operator (x+d/dx) has the eigen value α. Determine the corresponding wave function

A: If we let the eigen function is f(x) and eigen operator is ( x +d/dx ) having eigen value α, then we…

Q: The energy required for the excitation from the 2nd to the 3rd excited levels in a particle moving…

Q: To what speed must a proton be accelerated from rest for it to have a de Broglie wavelength of 100…

A: Given: Wavelength = 100 pm or 1×10-10 m The de Broglie wavelength is given by the expression: λ = hp…

Q: Consider a single particle with rest mass m residing in a one-dimensional space, x. = o for x a,…

Q: What values of J may occur in the terms (i) 3D, (ii) 4D, (iii) 2G? How many states (distinguished by…

A: A term symbol is represented as 2S+1LJ J can take the values from L+S to L-S L = 0 for S L = 1 for…

Q: (a) For a particle in the stationary state n of a one dimensional box of length a, find the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find an expression for the value of n of a particle of mass m in a one-dimensional box of length L…

A: For a one-dimensional box, energy is given as: En = n2h28ml2 The symbols stand for: En = Energy of…

Q: 3.2 Consider an assembly of six indistinguishable particles obeying Bose-Einstein statistics. The…

A: The solution of the given question is

Q: Consider a particle in a cubic box. What is the degeneracy (1,2,3, etc) of the level that has an…

A: The energy of a particle present in a cubic box is given by the expression (1) in which E is the…

Q: A particle rotating on the surface of a sphere with fixed r has the quantum numbers I = 3 and mj =…

A: The answer is given as follows The orbital angular momentum of the rotating particle is given by the…

Q: Which of these choices is the expectation value of momentum p for a particle in the state n = 5 in a…

A: The reasonable expected value of the result of an experiment is known as its expected value.

Concept explainers

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Techniques and Applications of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?
For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0 xa/4. (b) Calculate this probability for n = 1, 2, and 3
A glow-worm of mass 5.0 g emits red light (650 nm) with a power of 0.10 W entirely in the backward direction. To what speed will it have accelerated after 10 y if released into free space and assumed to live?
Calculate the probability of finding the particle in a one-dimensional box of length a in the interval 0.100a to 0.250a.
For a particle in a box of length L and in the state with n = 3, at what positions is the probability density a maximum? At what positions is the probability density zero?
A particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized wavefunction ψ(x) = a1/2e–ax/2, where a is a constant. Evaluate the expectation value of the position operator.
How fast would a particle of mass 1.0 g need to travel to have the same linear momentum as a photon of rad iation of wavelength 300 nm?
What are the implica tions of the uncertainty principle?
To what speed must a proton be accelerated for it to have a de Broglie wavelength of 3.0 cm?
The speed of a certain proton is 0.45 Mm s−1. If the uncertainty in its momentum is to be reduced to 0.0100 per cent, what uncertainty in its location must be tolerated?
By considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a particle in a ring with different values of the quantum number ml are mutually orthogonal.
Calculate the probability that a particle will be found in a tiny slice of space between 0.49L and 0.51L in a box of length L (defined in the interval (0,L) ) when it is in quantum state n = 1. For simplicity of integration, take the wavefunction to have a constant value equal to its midpoint value in the range given.