Answered: For a 1.0 x 10^-26 g particle in a box…

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 probability that the x coordinate is between 1.6000 and 1.6001 Å

Chemistry for Engineering Students

4th Edition

ISBN:9781337398909

Author:Lawrence S. Brown, Tom Holme

Publisher:Lawrence S. Brown, Tom Holme

Chapter5: Gases

Section: Chapter Questions

Problem 5.22PAE

See similar textbooks

Related questions

Q: Given that the wavelengths of the first three lines of the Balmer series are 656.2, 486.1, and 434.0…

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: 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: Calculate the lowest three energy level of a particle of mass 10-26kg in a box of length L=10-9m

A: The expression of energy in 1-D box is shown below: E =n2h28ml2 where; n = principle quantum number…

Q: What should be the speed of a beam of particles of mass 9.25×10-28 g in order to have a wavelength…

A: Given : Mass of particles = 9.25 X 10-28 g = 9.25 X 10-31 Kg (since 1…

Q: Write the steady-state symbol for the following atoms 11Na , 37Rb , 55Cs , 87Fr , 3Li

A: The ground state term symbol is generally represented as, 2S+1LJ Where, S is the total spin quantum…

Q: What must the kinetic energy in J of a small metal sphere with a mass of 2.50 × 10(-4) kg be so that…

A: The relation between the wavelength of the particle, mass of the particle, and velocity of the…

Q: The kinetic energy of an electron is (Z + 1.5)keV. momentum of the electron.

Q: The speed of a certain electron is 995 km s−1. If the uncertainty in its momentum is to be reduced…

A: According to Heisenberg’s uncertainty principle, if the accurate momentum of particle is known, its…

Q: D. Write down, but do not attempt to solve, the expression for the probability that an electron in a…

A: The limit will be from 2A to infinity in this case.

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: How fast must a 142-g baseball travel in order to have ade Broglie wavelength that is equal to that…

A: Given : mass of baseball = 142 g And wavelength of baseball = λ = wavelength of a X-ray photon = 100…

Q: Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is…

A: The atomic mass of the Argon is 39.948 amu or 40.00 amu. 1 amu = 1.661×10-27 kg 40 amu = 6.64×10-26…

Q: At what speed must an electron travel to have a wavelength of 0.100Å?

A: By help of De - broglie equation, we can calculate the speed of electron. The formula is - ^ = h/mv…

Q: Highly excited atoms have electrons with large principal quantum numbers. Such Rydberg atoms have…

A: a) The energy level for an atom is given by the expression is as follows, The difference in energy…

Q: 1.30 What is the minimum uncertainty in the position of a hydrogen atom in a particle accelerator…

A: Using the Heisenberg uncertainty equation, minimum uncertainty in the position can be calculated.

Q: A proton in a linear accelerator has a de Broglie wavelength of 122pm. What is the speed of the…

Q: 2-What is the probability that the electron with the lowest energy in a box of 2.0 nm length is…

Q: For the particle in a box, in the first excited state, only one of the following answers could be…

Q: Which expression represents the boundary conditions for a particle in a box with 0 <x< a? O w(0) =…

A: For 1 D box In the boundary x=0 and x=a

Q: One of the most important practical results of black body radiation and the hypotheses of Max Planck…

A: A black body is an object that absorbs all electromagnetic radiation comes in contact with it. It…

Q: Compare the momentum of a photon with a wavelength of 9.7´10-11 m to that of a 142 g baseball with a…

Q: Calculate the velocity of a neutron whose de-broglie wavelength is 505 pm.

A: De-Broglie equation is given as,

Q: What is the numerical value of the total angular momentum (L) for an electron in the f sub-shell of…

Q: In an experiment, a student found that a maximum wavelength of 351 nm is needed to just dislodge…

Q: A quantum-mechanical particle of mass m is contained within a three-dimensional box with all sides…

A: In general, symmetry leads to degeneracy and for a cubic box for which each of the sides is of the…

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

A: A particle in one dimensional box is a basic quantum-mechanical approximation revealing the…

Q: Determine the velocity of a marble (m = 8.66 g) with a wavelength of 3.46 × 10 -33 m

A: Given Mass of marble = 8.66 gram wavelength = 3.46 × 10-33 meter Velocity = ?…

Q: How fast must a 145.9−g baseball travel in order to have a de Broglie wavelength that is equal to…

Q: The watt is a unit of power, equivalent to 1 joule per second. If a single solar panel can generate…

A: Solar panel power generated = 125 watts 1 watt = 1 J/sec Energy generated = 125 J/sec

Q: Find the of ψ123 for a three-dimensional particle in a box

Q: A photon has the same momentum as an electron moving with a speed of 2.0 x 10$ m/s. What is the…

Q: 4) Consider a particle in a 1D box in its ground state such that Þ(x) = Bsin (*) where Bis a…

A: The solution is as follows :

Q: A. Ultraviolet 10-8 to 10-7 meters B. X-ray 10-11 to 10-8 meters C. Gamma ray 10-16 to 10-11…

A: To calculate the region, it is required to calculate the wavelength, which can be done as,

Q: Calculate the speed of a comet if it is rotation about the Sun in circular orbit with radius…

Q: A particle with a mass of 1.08 x 10-27 kg has a DeBroglie wavelength of 1.007 x 10-10 What is its…

Q: How fast must a 144.9−g baseball travel in order to have a de Broglie wavelength that is equal to…

A: De-Broglie equation is given as,

Q: A particle has velocity that is 90.% of the speed of light. If the wavelength of the particle is 1.5…

A: The given data contains, Velocity = 90% = 0.9 wavelength = 1.5 x 10-15m.

Q: The wavelength of an electron exist in a * stable orbit n=1 is equal to

A: The radius of first Orbit is given by - r1 = r0 × n2 Here, r1 = radius of first Orbit = ? r0 =…

Q: The wavelength of an electron exist in a stable orbit n=1 is equal to *

A: Energy Level Available to the electron is = n=1 Every electron in atom has some binding energy…

Q: A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the…

Q: Estimate the de Broglie wavelength of an alpha particle that has a kinetic energy of 1.47 keV. ___m

A: The de Broglie wavelength is given by where h = Plank's constant = 6.626 X 10-34 Js p = momentum…

Q: if n= 5, the highest value of l is ?

A: Interpretation- To determine the highest value of l when n= 5 Concept- This question is based on…

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: An electron moves in a straight line with constant speed v1.1 x10 m/s which has been measured withı…

Q: A proton in a linear accelerator has a de Broglie wavelength of 142 pm . What is the speed of the…

Q: The velocity (m/s) of an electron with a de Broglie wavelength of 1.312 nm is:

A: De-Broglie wavelength of any particle is given by λ=hmv ; h = Plancks constant m =mass of electron…

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

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 probability that the x coordinate is between 1.6000 and 1.6001 Å

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 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

Indicate which of these expressions yield an eigenvalue equation, and if so indicate the eigenvalue. a ddxcos4xb d2dx2cos4x c px(sin2x3)d x(2asin2xa) e 3(4lnx2), where 3=3f ddsincos g d2d2sincosh ddtan
Calculate ⟨x⟩ and ⟨x⟩^2 for the n = 3 level of a particle in a box of length a.
For the particle in a box, in the first excited state, only one of the following answers could be correct for the the probability of finding a particle in the leftmost 20% of the box. Choose which one. O 0.353 O 0.153 0.253 0.200 O 0.800
particle is confined to a one-dimensional box of length L. Deduce the location of the posit ions with in the box at which the particle is most likely to be found when the quantum number of the particle is (a) n = 1. (b) n = 2. and(c) n = 3.
Use the References to access important values if needed for this question. Complete the following table for the function y = -6z + 26. 1 2 3 Submit
(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.
describe in words how R^2 and the volume function individually contribute to the radial probability function
Calculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10° m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J=1 kg.m's", 1.00 cV =1VC, leV = 1.602 x 10"J, 1J=6.242 x 10" eV, etc.). %3D %3D
The velocitites of an electron (me = 9.1 · 10-31 kg), a proton (mp = 1.7.10-27 kg), a ladybug (mbug = 50 mg) and the moon (mmoon = 7.3 1022 kg) could be determined with an uncertainty of velocity of Av = 1.8 mm/s. Calculate the uncertainty of space Ax.
Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 25 degrees C. a) Use the model of a particle in a box and assume the particle is at the state: n = nx = ny = nz, calculate n of the above system. b) What is the energy separation between the states (n, n, n) and (n + 1, n, n). c) Assume that all the energy of the particle is from kinetic energy. Calculate the de Broglie wavelength of the particle. d) Based on your answers above, would you treat this particle classically or quantumly? Explain your answer.
In the following PIB model, suppose /4²dx (from x₁ to x₂) = 0.65, /4²dy (from y₁ to y₂) = 0.89, /4²dx (from x3 to x4) = 0.33 and /4²dy (from y3 to y4) = 0.76. Find the total probability of finding the particle inside area 1 and area 2. 0 area 1 a. 0.800 O b. 0.829 O c. 2.630 d. 0.788 e. 0.891 X2 area 2 X4 a
(a) If the kinetic energy of an electron is known to liebetween 1.59 × 10-19 J and 1.61 × 10-19 J, what is thesmallest distance within which it can be known to lie?(b) Repeat the calculation of part (a) for a helium atominstead of an electron.