Hydrogen atom continuous spectrum

Figure 5.8 shows an illustration of the characteristic purple-pink glow produced by excited hydrogen atoms and the visible portion of hydrogen s emission spectrum responsible for producing the glow. Note how the line nature of hydrogens atomic emission spectrum differs from that of a continuous spectrum. 

The dual wave-particle model of light accounted for several previously unexplainable phenomena, but scientists still did not understand the relationships among atomic structure, electrons, and atomic emission spectra. Recall that hydrogens atomic emission spectrum is discontinuous that is, it is made up of only certain frequencies of light. Why are the atomic emission spectra of elements discontinuous rather than continuous Niels Bohr, a Danish physicist working in Rutherford s laboratory in 1913, proposed a quantum model for the hydrogen atom that seemed to answer this question. Bohr s model also correctly predicted the frequencies of the lines in hydrogens atomic emission spectrum. 

The purpose of this note is to call attention once more and to explain a continuous spectrum in hydrogen that has been observed by Horton and Davies and by Crew and Hulburt and others, and possessing the peculiar characteristic of occurring without the presence of either atomic or molecular lines. Horton and Davies observed that hydrogen at pressures less than 1 mm. of mercury became suffused with a blue glow when excited by electrons of less than 15 volts velocity. This glow was a continuous spectrum showing no trace of atomic or molecular lines. 

From the spectroscopic side it may be concluded that the same interpretation of the continuous spectrum exhibited by hydrogen-iodide may be adopted as was proposed for non-polar molecules that gaseous hydrogen-iodide dissociates in a single and elementary act after absorption of radiation into a normal hydrogen atom and an excited iodine atom. 

It divides into two categories. For E < 0 we obtain an infinite discrete sequence of bounded states for > 0 we obtain a continuous spectrum. Due to the similarity of (6.1.22) to the Z = 0 radial Hamiltonian of the hydrogen atom, the wave functions and energies can be computed analytically. For the bound state wave functions we obtain... 

ON THE CONTINUOUS SPECTRUM OF THE HYDROGEN ATOM By Paul S. Epstein and Morris Muskat Norman Bridge Laboratory of Physics, California Institute of Technology Communicated March 23, 1929... 

The purpose of the present paper is to obtain expressions for the intensifies in the continuous spectrum of atomic hydrogen suitable for numerical calculations. This purpose is accomplished by means of a new integral representation for the wave function in this special case. As examples of application, we calculate the absorption spectra of hydrogen beyond the limits of the Balmer and of the Lyman series as well as certain limiting values of the absorption. 

---