StarkEffect.ppt
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The Stark effect is the splitting and shifting of spectral lines in atoms and molecules due to an external electric field. Johannes Stark discovered the effect in 1913 when he observed the spectral lines of hydrogen split into symmetrically spaced components under an electric field. The amount of splitting or shifting is quantified as the Stark shift or splitting. The effect occurs due to the interaction of the electric field with the charged particles in the atom, causing a perturbation to the electron orbitals and thus changing the energy levels.
StarkEffect.ppt
- 1. @Asan Fizika @fizika_physics
- 2. What do we mean by stark effect ? The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. The amount of splitting or shifting is called the Stark splitting or Stark shift. In general, one distinguishes first- and second- order Stark effects. The first-order effect is linear in the applied electric field, while the second-order effect is quadratic in the field.
- 4. The Stark Effect is shown here in the splitting and shifting of spectral lines in hydrogen under the influence of an external electric field.
- 5. History of the Stark Effect When Zeeman discovered the effect of magnetic fields on the wavelengths of emitted spectra from an excited gas, the Zeeman effect, it sparked a search for a similar effect due to electric fields. For 15 years the search failed to show such an effect and as a matter of fact.
- 6. Experimental failure to find the effect of electric fields on emitted spectra was actually due to a very simple phenomenon. Excitation of atoms to show spectra was usually performed by passing an electric arc through a gas. The gas would be ionized allowing current to flow via motion of the freed electrons and collisions between electrons and ions or electrons and neutral atoms would excite the ions or atoms and then spectra would be visible as the ions or atoms decayed back down from their excited states. The problem is that applying an external electric field to this highly conductive gas
- 7. Johannes Stark, in 1913, recognized the importance of lowering the conductivity of the luminous gas in order to maintain a strong electric field within the gas. Stark observed with a spectroscope that the characteristic spectral lines, called Balmer lines, of hydrogen were split into a number of symmetrically spaced components.
- 8. Balmer series The Balmer series or Balmer lines in atomic physics, is the designation of one of a set of 6 different named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empirical equation discovered by Johann Balmer in 1885.
- 9. The Balmer series is characterized by the electron transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. The transitions are named sequentially by Greek letter: n=3 to n=2 is called H-α(656 nm), from n=4 to n= 2 is H-β(486 nm), from n=5 to n=2 is H-γ(434 nm), and from n=6 to n=2 is H-δ(410 nm). There are also multiple ultraviolet Balmer lines that have wavelengths shorter than 400 nm.
- 11. Figure in the previous slide shows the quantized orbits of the hydrogen atom for n= 1 through 5. Each orbit corresponds to a definite energy state of the atom. The straight lines originating on the n= 3, 4, and 5 orbits and terminating on the n= 2 orbit represent transitions in the Balmer series.
- 12. Later, it was discovered that when the Balmer series lines of the hydrogen spectrum were examined at very high resolution, they were closely spaced doublets. This splitting is called fine structure. It was also found that excited electrons from shells with n greater than 6 could jump to the n = 2 shell, emitting shades of ultraviolet when doing so.
- 13. Hydrogen Atom Ground State in an E-field, the Stark Effect. We have solved the Hydrogen problem with the following Hamiltonian Now we want to find the correction to that solution if an Electric field is applied to the atom. We choose the axes so that the Electric field is in the z- direction. The perturbation is then:
- 14. It is typically a small perturbation. For non-degenerate states, the first order correction to the energy is zero because the expectation value of z is an odd function. First order correction (n=1) : Since, To use perturbation theory, we’ll need the wave functions for unperturbed hydrogen, which are given in Griffiths as equation 4.89. For the ground state n = 1, we have
- 16. We therefore need to calculate the second order correction. This involves a sum over all the other states. We need to compute all the matrix elements of z between the ground state and the other Hydrogen states.
- 17. References: • H. Friedrich, Theoretical Atomic Physics, (1990). • E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra, (1935). • A. Sommerfeld , Atomic Structure and Spectral Lines, London: Methuen (1923). • H. E. White, Introduction to atomic spectra, (1934). • C. R. Nave, Hydrogen Spectrum, (2006). • J. Griffiths, David Introduction to Quantum Mechanics, 2nd Ed (2005). • A. McGraw-Hill, Perspectives of Modern Physics, (1969).