bartleby

Concept explainers

Question
Book Icon
Chapter 40, Problem 1P

(a)

To determine

The magnitude of de Broglie wavelength.

(a)

Expert Solution
Check Mark

Answer to Problem 1P

The de Broglie wavelength is 1.26×1010m.

Explanation of Solution

The angular wave number from the wave function is 5.00×1010m1.

Write the expression to calculate the wavelength.

  λ=2πk

Here, λ is the wavelength and k is the angular wave number.

Write the expression to calculate 5.00×1010m1 for k in the above equation to calculate λ.

  λ=2π5.00×1010m1=1.26×1010m

Conclusion:

Therefore, the de Broglie wavelength is 1.26×1010m.

(b)

To determine

The magnitude of momentum.

(b)

Expert Solution
Check Mark

Answer to Problem 1P

The magnitude of momentum is 5.26×1024kgm/s.

Explanation of Solution

Write the expression to calculate the momentum.

  p=hλ

Here, p is the momentum and h is the Planck’s constant.

Substitute 6.626×1034Js for h and 1.26×1010m for λ in the above equation to calculate p.

  p=6.626×1034Js1.26×1010m=5.26×1024kgm/s

Conclusion:

Therefore, the magnitude of momentum is 5.26×1024kgm/s.

(c)

To determine

The kinetic energy in electron volts.

(c)

Expert Solution
Check Mark

Answer to Problem 1P

The kinetic energy in electron volts is 95.0eV.

Explanation of Solution

Write the expression to calculate the kinetic energy.

  K=p22m

Here, K is the kinetic energy and m is the mass of electron.

Substitute 5.26×1024kgm/s for p and 9.11×1031kg for m in the above equation to calculate K.

  K=(5.26×1024kgm/s)22(9.11×1031kg)=1.52×1017J(1eV1.602×1019J)=95.0eV

Conclusion:

Therefore, the kinetic energy in electron volts is 95.0eV.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A free electron has a wave function                                            ψ(x) = Ae i(5.00×1010x)where x is in meters. Find its (a) de Broglie wavelength, (b) momentum, and (c) kinetic energy in electron volts.
A free electron moving along the x-direction (one for which V(x) = 0) would have a wave function of the form f(x) = A eikx + B e−ikx where A and B are constants. (a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm¯¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by p² ħ² d² Ĥ 2me 2me dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using Â, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity?
A free electron moving along the x-direction (one for which V(x) = 0) would have a wave function of the form f(x) = A eikx + Be -ikx where A and B are constants. (a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 x 10² m/sec, what is the value of k (in nm-¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by ħ² d² p² 2me 2m₂ dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using Â, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity? Ĥ = =
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
  • Text book image
    Modern Physics
    Physics
    ISBN:9781111794378
    Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
    Publisher:Cengage Learning
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning