Physical Chemistry , 1st ed.

time. Energy multiplied by time yields a quantity known as action. Earlier in history, scientists developed something called the ...

Assumption 1, regarding the relationship between forces, can be written as FcentFcoul (9.26) where Fcentand Fcoulare the centri ...

that has units of action can be related to h, and Bohr did just that. He assumed that the possible quantized values of the angul ...

substitute for the radius in the expression for the total energy, equation 9.31, to obtain Etot 8  m 2 0 n ee 2 4 h^2  (9.3 ...

Bohr stated that this Emust equal the energy of the photon: Eh (9.37) Now that Bohr had derived an equation for the total ene ...

where Zis the charge on the nucleus. So Bohr’s theory is applicable to U^91 , which has all but one of its electrons stripped f ...

but also their new directions of motion. If waves have particle properties, per- haps it is not too far-fetched to consider that ...

For the electron:  2.43 10 ^10 m or 2.43 Å The de Broglie wavelength of the automobile is unnoticeable even using modern m ...

atoms behaved in the manner described by Newton, and they don’t. Individual electrons and atoms require a different model to exp ...

9.2 Laws of Motion 9.1.For an object having mass mfalling in the zdirection, the kinetic energy is 2 ^1 mz ̇^2 and the potenti ...

9.21.Integrate Planck’s law (equation 9.23) from the wave- length limits 0 to to get equation 9.24. You will have to rewrit ...

10 273273 N EW DISCOVERIES PROMPTED THE NEED for a better theory to de- scribe the behavior of matter at the atomic level, as in ...

ideas will be discussed in detail in the sections that follow. Briefly, however, it might be useful to summarize these ideas so ...

Single-valued (that is, a wavefunction must have only one possible F(x) value for each and every value ofx.) Continuous Differe ...

10.3 Observables and Operators When studying the state of a system, one typically makes various measurements of its properties, ...

Example 10.2 For each of the following combinations of operator and function, write the complete mathematical operation and eval ...

Example 10.3 Which of the following operator/function combinations would yield eigen- value equations? What are the eigenvalues ...

The postulate regarding eigenfunctions and eigenvalue equations gets more specific: the only possiblevalues of the observables a ...

Heisenberg (Figure 10.2), who announced it in 1927. The uncertainty principle states that there are ultimate limits to how exact ...

x (1000 kg)(1 m/s)  6.626 2 2 1 0  (^34) J s where all of the values of the variables have been substituted into equation 10 ...