Concept explainers
(a)
The electric forces on the electron and on the proton.
(a)
Answer to Problem 126P
The electric force on the electron is
Explanation of Solution
Write the equation for the magnitude of the electric force using Coulomb’s law.
Here,
Conclusion:
The value of
Substitute
The force on electron will be toward the proton and the force on proton will be toward the electron.
Therefore, the electric force on the electron is
(b)
The electron’s acceleration and speed.
(b)
Answer to Problem 126P
The electron’s acceleration is
Explanation of Solution
The electric force is the net force acting on the electron.
Write the equation for the net force.
Here,
Rewrite the above equation for
The net force provides the centripetal force for the motion of the electron.
Write the equation for the centripetal force on the electron.
Here,
Equate equations (II) and (IV) and rewrite it for
Conclusion:
The mass of electron is
Substitute
Substitute
Therefore, the electron’s acceleration is
(c)
The minimum amount of energy required to ionize the atom if it stars in the ground state.
(c)
Answer to Problem 126P
The minimum amount of energy required to ionize the atom if it stars in the ground state is
Explanation of Solution
The minimum energy required to ionize the atom will be equal to the total energy of the atom. The total energy of the atom is the sum of the kinetic energy of the electron and the electric potential energy of the atom.
Write the equation for the total energy of atom.
Here,
Write the equation for
Write the equation for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the minimum amount of energy required to ionize the atom if it stars in the ground state is
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Chapter 17 Solutions
Physics
- The gravitational force between two masses m and m2 located a distance r apart has a magnitude of FG =Gmm2, where G = 6.674×10 N ⋅ m2/kg2; this has a nearly identical form to the Coulomb force law between two charges (except the force constants are different and masses are always positive). Suppose two identical spherical masses with radius a = 30 μm and mass density ρm = 2.2 × 103 kg/m3 are located a distance L apart. If they are released rest, their gravitational attraction will cause them to eventually collide. If, however, each mass has the same charge, then a Coulomb force will oppose the gravitation force. Suppose each mass has an excess of n extra electrons that causes both to be negatively charged. Find the minimum number n that would prevent the masses from colliding.arrow_forwardIn one model of the hydrogen atom, the electron revolves in a circular orbit of radius 5.3 x 10-11 m. Calculate the speed of the electron.arrow_forwardTwo Plutonium atoms (atomic mass = 244) both gain 2 electrons each. Draw a FBD and calculate the net force (consider both Fg and FQ) between these two Pu ions which are 1.0 nm apart.arrow_forward
- A hydrogen atom when in its lowest energy state consists of a proton nucleus of charge +e (remember that +e = 1.6 x 10-19 C) and an electron of charge -e and mass of 9.1 x 10-31 kg. In the Bohr model of the atom, the electron moves around the nucleus in an approximately circular orbit with a radius of 0.52 x 10-10 m. The speed of the electron when in this lowest energy orbit is approximately 2.3 x 106 m/s. Imagine that we want to ionize this atom (that is free up the electron from its nucleus) by launching ANOTHER electron at the atom to break it apart. If we were to launch this electron from very far away from the atom, then how fast must it be launched in order to break apart the atom, so that all three particles (the proton and two electrons) end up at rest, very far apart?arrow_forwardThe electron in a hydrogen atom is initially at a distance2.12 Å from the proton, and then moves in the +x direction to a distance 0.529 Å from the proton.(a) Calculate the magnitude of the force on the electronat each separation.(b) Calculate the change in the potential energy betweenthe proton and the electron.(c) Calculate the change in the speed of the electron if theelectron was initially stationary.arrow_forwardOrbital plane change: A satellite is launched due east from the Kennedy Space Center (latitude 28.6º). Following orbit insertion and a circularizing second burn with no plane change, the satellite is in a circular orbit at an altitude of 540 km. Its final destination is a circular orbit at 15,000 km with an inclination of 0 degrees. a. Using two Hohmann transfers, what total Δv is required to move the satellite from the initial orbit to the higher circular at the same inclination? Include a sketch showing the initial orbit, the transfer orbit and the final orbit. Include the location(s) of the burn(s). b. Calculate the Δv required to change the orbital inclination from its initial value to zero degrees in both the initial circular orbit and the higher circular orbit. Where would you want to make the change to the orbital inclination?arrow_forward
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- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University