Physical Chemistry , 1st ed.

several phenomena could not be explained by the scientific thinking of the 1800s. Most of these phenomena were based on the prop ...

This means that Newton’s second law can be written Fmd dt (^2) x  2 (9.3) It is not uncommon to ignore the vector character o ...

derivative with respect to time, and so on). Further, if the potential energy V is a function only of position, that is, the coo ...

The utility of the Hamiltonian function depends on the kinetic energy K, which is a function of the time derivatives of position ...

which can be rearranged algebraically to yield the second-order differential equation d dt (^2) x  2 m kx 0 This different ...

Since we are confining motion to one dimension, only one momentum needs to be defined. Using the Lagrangian defined above, we ca ...

important, the other forms are more appropriate to use. We will find later that for atomic and molecular systems, the Hamiltonia ...

its component colors and pass this colored light through a chemical sample. The sample absorbed some wavelengths of light, not o ...

sample was energetically stimulated so that it emitted light). Many of these spectra were complicated, but for some reason the s ...

mathematical formula. The fact that the spectrum of hydrogen was so simple and so unexplainable caused a problem for classical m ...

Although the nuclear atom fit the dramatic results of the experiment, there was a major problem: According to Maxwell’s electrom ...

The study of radioactivity, beginning with Antoine-Henri Becquerel’s dis- covery in 1896, was another problem relating to atomic ...

different wavelengths of light emitted were measured and plotted. The inten- sity distribution presented much fuel for debate. T ...

where the value of this constant is approximately 2898 mK; the wave- length is in units of micrometers. This equation, enuncia ...

Example 9.4 A lightbulb filament at 2500 K emits light having a maximum intensity at what wavelength? Solution Using the Wien di ...

body radiation, but none were any more successful than the Rayleigh-Jeans law. The matter remained unsolved until 1900. All of t ...

then used statistics to derive an expression for the energy density distribution of blackbody radiation. The modern form of the ...

where is the total power flux(in units of J/m^2 s, or W/m^2 ) and the constants have their usual meaning. The groups of consta ...

Example 9.5 a.What is the energy of one quantum of light that has a wavelength of 11,592 Å? You will need to use the relationshi ...

Solution Calculating the energy of the light: E(6.626 10 ^34 Js)(4.77 1015 s^1 ) E3.16 10 ^18 J Using Einstein’s equati ...