27 : 2/ Quantum Mechanical Basis of Molecular Spectra 503 



of diffraction and interference emphasize that light is transmitted as a 

 wave. (This does not mean that something is wiggling or waving back 

 and forth. Rather, it means that the transmission of light obeys the 

 same type of descriptive equations as do elastic waves which one can see 

 and feel.) However, the radiation from black bodies and the photo- 

 electric effect can only be explained by assuming that electromagnetic 

 energy is emitted and absorbed in finite chunks called photons. Each 

 photon has an energy E which is related to the frequency of the trans- 

 mitted wave by 



E = hv (1) 



In this, h is Planck's constant and v is the frequency. The numerical 

 value of h is 6.6 x 10 " 27 erg -sec. In general, the wavelength A rather 

 than v is measured in diffraction and interference experiments. Accord- 

 ingly, Equation 1 is often rewritten 



he 

 E = * (2) 



Thus, light behaves in transmission as a wave, but in absorption and in 

 emission as a particle. 



Electrons also exhibit this apparent duality. In experiments such as 

 those in which the charge e on an electron is measured, the electron 

 acts as a particle. It can be accelerated; it can possess kinetic energy; 

 and in many other ways it can act as a particle obeying Newton's laws of 

 motion. There are other experiments however, which cannot be 

 explained in terms of the particle-like properties of electrons. For 

 example, electrons exhibit interference when reflected by a crystal, and 

 their transmission through an electron microscope can be described 

 accurately through the use of the phenomenon of diffraction. When 

 treated as a wave, their wavelength is given by 



X=\ (3) 



P 



and their frequency by 



V = 



E 



~h 



where p is the momentum and where E is the total relativistic energy 

 me 2 . Thus, just as photons are, electrons also are transmitted as a wave 

 but act in many places as particles. 



These apparent dualities can be resolved by treating both matter and 

 electromagnetic energy as made up of small particles, that is, both are 

 quantized. These particles do not individually obey Newton's laws of 



