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Chapter 39: Q37P (page 1216)

A neutron with a kinetic energy of 6.0 eV collides with a stationary hydrogen atom in its ground state. Explain why the collision must be elastic鈥攖hat is, why kinetic energy must be conserved. (Hint: Show that the hydrogen atom cannot be excited as a result of the collision.)

Short Answer

Expert verified

The neutron, with a kinetic energy of 6.0 eV does not have enough energy to excite the hydrogen atom.

Step by step solution

01

The energy of the photon emitted by a hydrogen atom:

The expression of the energy of the photon emitted for a hydrogen atom jumps from a state of to is given by,

E=13.6eV(1n12-1n12) 鈥�.. (1)

02

Explain the reason why the collision must be elastic and kinetic energy must be conserved

Substitute for and for in equation (1).

E=13.6eV1(1)2-1(2)2=13.6eV34=10.2eV

This is the minimum energy that the hydrogen atom can accept in order to jump to the first excited state. The neutron, with a kinetic energy of does not have enough energy to excite the hydrogen atom, therefore all the kinetic energy of the neutron will be transferred to the hydrogen atom as kinetic energy in form of an elastic collision.

Hence, the collision must be elastic and kinetic energy must be conserved.

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Most popular questions from this chapter

In atoms, there is a finite, though very small, probability that, at some instant, an orbital electron will actually be found inside the nucleus. In fact, some unstable nuclei use this occasional appearance of the electron to decay by electron capture. Assuming that the proton itself is a sphere of radius 1.1脳10-15mand that the wave function of the hydrogen atom鈥檚 electron holds all the way to the proton鈥檚 center, use the ground-state wave function to calculate the probability that the hydrogen atom鈥檚 electron is inside its nucleus.

Figure 39-9 gives the energy levels for an electron trapped in a finite potential energy well 450 eV deep. If the electron is in the n = 3 state, what is its kinetic energy?

Consider a conduction electron in a cubical crystal of a conducting material. Such an electron is free to move throughout the volume of the crystal but cannot escape to the outside. It is trapped in a three-dimensional infinite well. The electron can move in three dimensions so that its total energy is given by

E=h28L2m(n12+n22+n32)

in whichare positive integer values. Calculate the energies of the lowest five distinct states for a conduction electron moving in a cubical crystal of edge length L=0.25渭m.

An old model of a hydrogen atom has the chargeof the proton uniformly distributed over a sphere of radiusa0, with the electron of charge -eand massat its center.

  1. What would then be the force on the electron if it were displaced from the center by a distancer鈮�a0?
  2. What would be the angular frequency of oscillation of the electron about the center of the atom once the electron was released?

In a simple model of a hydrogen atom, the single electron orbits the single proton (the nucleus) in a circular path. Calculate

  1. The electric potential set up by the proton at the orbital radius of52.0 pm
  2. The electric potential energy of the atom,
  3. The kinetic energy of the electron.
  4. How much energy is required to ionize the atom (that is, to remove the electron to an infinite distance with no kinetic energy)? Give the energies in electron-volts.
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