The Energy Levels of Hydrogen

Each photon of blue light carries a larger quantity of energy than a photon of red light. 

A particular color (wavelength) of light carries a particular amount of energy per photon. 

I AIM To understand how the emission spectrum of hydrogen demonstrates the quantized nature of energy. 

As we learned in the last section, an atom with excess energy is said to he in an excited state. An excited atom can release some or all of its excess energy by emitting a photon (a particle of electromagnetic radiation) and thus move to a lower energy state. The lowest possible energy state of an atom is called its ground state. 

Some H atoms absorb energy and become excited 

We can learn a great deal about the energy states of hydrogen atoms by observing the photons they emit. 

Recall that a beam of red light has lower-energy photons than a beam of blue light. 

When a hydrogen atom absorbs energy from some outside source, it uses this energy to enter an excited state. 

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In Exercises 15-2 and 15-3 you observed that the energy levels of hydrogen vary systematically with the quantum (or notch) number. The... 

The ionization potential appears to reduce sharply towards zero with decrease of the ion sphere radius indicating the effect of increased plasma coupling strength. Table 1 gives the energy levels of hydrogen-like Ne in a plasma environment for different plasma densities. 

An important generalization of the quantum theory by Sommerfeld [125] and independently by Wilson [142] allowed a detailed study of the non-radiating non-circular orbits, and led to Sommerfeld s celebrated fine structure formula which represents the energy levels of hydrogen-like atoms to a precision which was substantiated by the most refined experiments over the twenty years following its derivation. Comparison with experiment, however, implies a consideration, not only of energy levels, but also of the relative intensities of spectral lines. We shall see that on this point the theory failed. 

Rydberg constant - The fundamental constant which appears in the equation for the energy levels of hydrogen-like atoms i.e., = hcR where h is Planck s constant, c... 

So we can conclude that all hydrogen atoms have the same set of discrete energy levels. We say the energy levels of hydrogen are quantized. That is, only certain values are allowed. Scientists have found that the energy levels of all atoms are quantized. 

What experimental evidence do scientists have that the energy levels of hydrogen are quantized ... 

Light is emitted from the hydrogen atom only at certain wavelengths. If the energy levels of hydrogen were continuous, a hydrogen atom would emit energy... 

Rydberg constant (R - The fundamental constant which appears in the equation for the energy levels of hydrogen-like atoms i.e., E = hcR. 2 JrP-, where h is Planck s constant, c the speed of light, Z the atomic number, (Xthe reduced mass of nucleus and electron, and n the principal quantum number (n = 1,2,. ..). 

The energy levels of hydrogen (and other atoms) are, which means that only certain values of energy are allowed. 

Energy is emitted at wavelengths corresponding to specific transitions for the electron among the energy levels of hydrogen. 

H. Grotch, D. R. Yennie. Effective Potential Model for Calculating Nuclear Corrections to the Energy Levels of Hydrogen. Rev. Mod. Phys., 41 (1969) 350 74. 

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