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Chapter 8: Q13P (page 344)

The Frank Hertz experiment involved shooting electrons into a low density gas of mercury atoms and observing discrete amounts of kinetic energy loss by the electrons. Suppose that instead the similar experiment is done with a very cold gas of atomic hydrogen, so that all of the hydrogen atoms are initially in ground state. If the kinetic energy of an electron is 11.6 eV just before it collides with a hydrogen atom. How much kinetic energy will the electron have just after it collides with and excites the hydrogen atom?

Short Answer

Expert verified

The kinetic energy of electron after collision is1.4eV .

Step by step solution

01

Identification of given data

The kinetic energy of electron just before collision isKi=11.6eV

02

Conceptual Explanation

The electron loses it kinetic energy just after collision with atomic hydrogen and kinetic energy of electron just after collision will be equal to the difference between kinetic energy before collision and energy of hydrogen atom in first excited state.

03

Determination of kinetic energy of electron after collision

The kinetic energy of electron just after collision is given as:

Kf=Ki-Ee

Here, Ee is the energy of hydrogen in first excited state and its value is 10.2eV

Substitute all the values in the above equation.

Kf=11.6eV-10.2eVKf=1.4eV

Therefore, the kinetic energy of electron just after collision is 1.4eV.

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Most popular questions from this chapter

A bottle contains a gas with atoms whose lowest four energy levels are -12eV, -6eV, -3eV, and -2eV. Electrons run through the bottle and excite the atoms so that at all times there are large numbers of atoms in each of these four energy levels, but there are no atoms in higher energy levels. List the energies of the photons that will be emitted by the gas.

Next, the electron beam is turned off, and all the atoms are in the ground state. Light containing a continuous spectrum of photon energies from 0.5eVto 15eVshines through the bottle. A photon detector on the other side of the bottle shows that some photon energies are depleted in the spectrum (鈥渄ark lines鈥�). What are the energies of the missing photons?

Summarize the differences and similarities between different energy levels in a quantum oscillator. Specifically for the first two levels in figure 8.26, compare the angular frequency Ks/m, the amplitude , and the kinetic energyk at the same value of . ( In a quantum-mechanical analysis the concepts of angular frequency and amplitude require reinterpretation. Nevertheless, there remain elements of the classical picture. For example, larger amplitude corresponds to a higher probability of observing a large stretch.)

Assume that a hypothetical object has just four quantum states, with the energies shown in Figure 8.43.

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The mean lifetime of a certain excited atomic state is 5 ns. What is the probability of the atom staying in this excited state for t=10 ns or more?
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