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Chapter 39: Q36P (page 1216)

(a) What is the energy E of the hydrogen-atom electron whose probability density is represented by the dot plot of Fig. 39- 21? (b) What minimum energy is needed to remove this electron from the atom?

Short Answer

Expert verified
  1. The energy of the hydrogen-atom electron is -3.4eV.
  2. The required energy is 3.4eV.

Step by step solution

01

The energy E of the hydrogen-atom electron:

The expression of the energy is given by,

E=13.6eVn2 鈥�.. (1)

Here, nis the number of states.

02

(a) Find the energy E of the hydrogen-atom electron:

Substitute 2 for n in equation (1).

E=-13.6eV22=-3.4eV

Therefore, the energy of the hydrogen-atom electron is -3.4eV.

03

(b) Find the minimum energy is required to remove the electron from the atom:

The energy of the photon emitted for a hydrogen atom jumps from a state of n1to n2is given by,

E=13.6eV1n12-1n22

Substitute 2 for n1and 鈭�for n2in equation (2).

E=13.6eV122-1鈭�2=3.4eV

Hence, the required energy is 3.4eV.

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Most popular questions from this chapter

Let 鈭�Eadj be the energy difference between two adjacent energy levels for an electron trapped in a one-dimensional infinite potential well. Let E be the energy of either of the two levels. (a) Show that the ratio 鈭�Eadj/E approaches the value at large values of the quantum number n. As n鈫�鈭�, does (b) 鈭�Eadj (c) E or, (d) 鈭�Eadj/E approaches zero? (e) what do these results mean in terms of the correspondence principle?

Figure 39-25 shows three infinite potential wells, each on an x axis. Without written calculation, determine the wave function 蠄for a ground-state electron trapped in each well.

Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with L=1.4脳10-14, a typical nuclear diameter. What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

An electron is confined to a narrow-evacuated tube of length 3.0 m; the tube functions as a one-dimensional infinite potential well. (a) What is the energy difference between the electron鈥檚 ground state and its first excited state? (b) At what quantum number n would the energy difference between adjacent energy levels be 1.0 ev-which is measurable, unlike the result of (a)? At that quantum number, (c) What multiple of the electron鈥檚 rest energy would give the electron鈥檚 total energy and (d) would the electron be relativistic?

In the ground state of the hydrogen atom, the electron has a total energy of -13.06 eV. What are (a) its kinetic energy and (b) its potential energy if the electron is one Bohr radius from the central nucleus?
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