(a)
The electron would be in equilibrium at centre and if displaced would experience a restoring force.
(a)
Answer to Problem 24.62CP
The electron would be in equilibrium at centre and if displaced would experience a restoring force of magnitude
Explanation of Solution
Given info:
Consider the field distance
Write the expression of Guass’s law.
Here,
Write the expression for area of sphere.
Here,
Substitute
Write the expression for electric charge.
Here,
Substitute
Write the expression for volume of sphere.
Write the expression for density of sphere.
Here,
Substitute
Substitute
So,
The above electric field is directed outward.
The expression for the force is,
Substitute
Conclusion:
Therefore, the electron would be in equilibrium at centre and if displaced would experience a restoring force of magnitude
(b)
To show: The constant
(b)
Answer to Problem 24.62CP
The constant
Explanation of Solution
Given info:
Write the expression for spring force.
Here,
Also, the field force is,
Equate the above two force equations.
Substitute
Conclusion:
Therefore, the constant
(c)
The expression for the frequency
(c)
Answer to Problem 24.62CP
The expression for the frequency
Explanation of Solution
Given info:
According to Newton’s second law of motion,
Here,
Also, the field force is,
Equate the above two force equations.
Rearrange the above equation to get
Compare the above equation with the simple harmonic wave equation which is,
Equate the above two acceleration equations.
From the above equation
Write the general expression for frequency of
Substitute
Substitute
Conclusion:
Therefore, the expression for the frequency
(d)
The value of radius of orbit.
(d)
Answer to Problem 24.62CP
The value for
Explanation of Solution
Given info:
Write the expression for frequency
Rearrange the above equation to get
Substitute
Conclusion:
Therefore, the value for
Want to see more full solutions like this?
Chapter 24 Solutions
PHYSICS F/...V.1 (LL)-W/ACCESS >CUSTOM<
- In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å:(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton. (b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)? (c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06 Å separation?arrow_forwardThe spherical nucleus of the certain atom contains a positive charge ze in a volume of radius r. compare the force exerted on electron inside the nucleus at radius 0.5r with the force at radius r for the nucleus in which a)the charge quantity is constant throughout its volume and b)the charge density increases in direction proportion to the radius r. ?arrow_forward(a) What is the magnitude of the angular momentum for an l = 1 electron? (b) Calculate the magnitude of the electron’s spin angular momentum. (c) What is the ratio of these angular momenta?arrow_forward
- | Electric fields in the atom. (a) Within the nucleus. What strength of electric field does a proton produce at the distance of another proton, about 5.0 * 10-15 m away? (b) At the electrons. What strength of electric field does this proton produce at the dis - tance of the electrons, approximately 5.0 * 10-10 m away?arrow_forwardHow much work is required to set up the four-charge configuration of the figure if q = 8.35 pC, a = 67.9 cm, and the particles are initially infinitely far apart and at rest?arrow_forwardIn the classical model of a hydrogen atom, an electron orbits a proton with a kinetic energy of +13.6 eV and an electric potential energy of −27.2 eV. HINT (a) Use the kinetic energy to calculate the classical orbital speed (in m/s). m/s (b) Use the electric potential energy to calculate the classical orbital radius (in m). marrow_forward
- An electron is in the hydrogen atom with n = 5. (a) Find the possible values of L and Lz for this electron, in units of h. (b) For each value of L, find all the possible angles between L → and the z-axis. (c) What are the maximum and minimum values of the magnitude of the angle between L →and the z-axis?arrow_forwardIf an electron in an atom has orbital angular momentum with values limited by 3, how many values of (a) Lorb,z and (b) morb,z can the electron have? In terms of h,m, and e, what is the greatest allowed magnitude for (c) Lorb,z and (d) morb,z? (e) What is the greatest allowed magnitude for the z component of the electron’s net angular momentum (orbital plus spin)? (f) How many values (signs included) are allowed for the z component of its net angular momentum?arrow_forwardWhat is the largest angle in degrees that L can make with the z-axis for an l=3 electron? Round your answer to one decimal place.arrow_forward
- On an infinite non-conductive surface with a surface charge density of σ = +5 pC / m² we open a hole of radius R. The z axis is perpendicular to the surface and passes through the center O of the hole. Calculate the intensity of the electric field (vector) in Σ (OΣ = 2.56 cm)arrow_forward1.9 * 10 ^ 5 Nm^2/C LEAVING THE SURFACE IS ANSWER GIVEN IS IT CORRECT OR WRONG .... MAKE A SUITABLE DIAGRAM AND PLEASE EXPLAIN IT LITTLE BIT ....AND MORE SUBPART What is the value of angular momentum of electron in the second orbit of Bohr’s model of hydrogen atom?arrow_forwardFrom which atom of each of the following pairs is it easier to remove an electron: (a) krypton or bromine, (b) rubidium or cerium, (c) helium or hydrogen?arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax