
Concept explainers
(a)
Plot of wave function as a function of
(a)

Answer to Problem 74P
The wave function was plotted as a function of
Explanation of Solution
Write the given wave function of the electron.
Here,
Write the formula to calculate the probability of finding a particle in a certain range.
Here,
Refer equation (I) and plot the wave function as a function of
Figure 1 below shows the plot of wave function.
Conclusion:
The wave function was plotted as a function of
(b)
Plot of probability density as a function of
(b)

Answer to Problem 74P
The probability density was plotted as a function of
Explanation of Solution
Write the given wave function of the electron.
Here,
Write the formula to calculate the probability of finding a particle in a certain range.
Here,
Refer equation (II) and plot the probability density as a function of
Figure 2 below shows the plot of wave function.
Conclusion:
The probability density was plotted as a function of
(c)
To show that
(c)

Answer to Problem 74P
The
Explanation of Solution
Write the given wave function of the electron.
Here,
For the wave function to be a reasonable wave function, there are set of condition.
The
As
The
The
Conclusion:
The
(d)
To normalize the wave function.
(d)

Answer to Problem 74P
The normalization constant of the given wave function is
Explanation of Solution
Write the given wave function of the electron.
Here,
Write the condition for normalized wave function.
The wave function is symmetric. Thus re-write the above condition.
Substitute equation (I) in the above equation.
Conclusion:
The normalization constant of the given wave function is
(e)
The probability of finding the electron in the range
(e)

Answer to Problem 74P
The probability of finding the particle in the range
Explanation of Solution
Refer section (d) and write the given normalized wave function of the electron.
Here,
Write the formula to calculate the probability of finding a particle in a certain range.
Here,
Refer equation (II) in equation (III) to determine probability in range
Conclusion:
The probability of finding the particle in the range
Want to see more full solutions like this?
Chapter 28 Solutions
Principles of Physics: A Calculus-Based Text
- The human eye is most sensitive to light having a frequency of about 5.5 × 1014 Hz, which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fit across a distance of 2.2 cm?arrow_forwardA one-dimensional harmonic oscillator of mass m and angular frequency w is in a heat bath of temperature T. What is the root mean square of the displacement of the oscillator? (In the expressions below k is the Boltzmann constant.) Select one: ○ (KT/mw²)1/2 ○ (KT/mw²)-1/2 ○ kT/w O (KT/mw²) 1/2In(2)arrow_forwardTwo polarizers are placed on top of each other so that their transmission axes coincide. If unpolarized light falls on the system, the transmitted intensity is lo. What is the transmitted intensity if one of the polarizers is rotated by 30 degrees? Select one: ○ 10/4 ○ 0.866 lo ○ 310/4 01/2 10/2arrow_forward
- Before attempting this problem, review Conceptual Example 7. The intensity of the light that reaches the photocell in the drawing is 160 W/m², when 0 = 18°. What would be the intensity reaching the photocell if the analyzer were removed from the setup, everything else remaining the same? Light Photocell Polarizer Insert Analyzerarrow_forwardThe lifetime of a muon in its rest frame is 2.2 microseconds. What is the lifetime of the muon measured in the laboratory frame, where the muon's kinetic energy is 53 MeV? It is known that the rest energy of the muon is 106 MeV. Select one: O 4.4 microseconds O 6.6 microseconds O 3.3 microseconds O 1.1 microsecondsarrow_forwardThe Lagrangian of a particle performing harmonic oscil- lations is written in the form L = ax² - Bx² - yx, where a, and are constants. What is the angular frequency of oscillations? A) √2/a B) √(+2a)/B C) √√Ba D) B/αarrow_forward
- The mean temperature of the Earth is T=287 K. What would the new mean temperature T' be if the mean distance between the Earth and the Sun was increased by 2%? Select one: ○ 293 K O 281 K ○ 273 K 284 Karrow_forwardTwo concentric current-carrying wire loops of radius 3 cm and 9 cm lie in the same plane. The currents in the loops flow in the same direction and are equal in magnitude. The magnetic field at the common center of the loops is 50 mT. What would be the value of magnetic field at the center if the direction of the two currents was opposite to each other (but their value is kept constant)? Select one: ○ 20 mT ○ 10 mT O 15 mT ○ 25 mTarrow_forwardAn ideal coil of inductivity 50 mH is connected in series with a resistor of 50 ohm. This system is connected to a 4.5 V battery for a long time. What is the current in the circuit? Select one: O 45 mA ○ 90 mA 00 mA O 150 mAarrow_forward
- There are two thin-walled spherical shells made from the same material, the radius of the smaller shell is half of the radius of the larger one. The thickness of the walls is the same. Denote the moment of inertia (with respect to the center) of the larger shell by I₁, and that of the smaller one by 12. What is the ratio I₁/12? Select one: ○ 8 O 16 O 4 ○ 32arrow_forwardA swimming pool has dimensions 20.0 m X 20.0 m and a flat bottom. The pool is filled to a depth of 3.00 m with fresh water. By what force does the water push each of the sidewalls? Density of water is 1000 kg/m³. Select one: ○ ~ 900 KN о ~ 2 ~ 1800 kN 600 kN 1500 kNarrow_forwardFrom one corner of a thin homogeneous square metal sheet with sides of L = 20 cm is cut an L/2 square sheet as shown in the figure. Approximately how far away is the centre of mass of the resulting shape from the centre P of the original square? P ○ 24 mm ○ 42 mm ○ 32 mm ○ 16 mmarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill





