Wave Nature of Light-De-Broglie Wavelength of an Electron

Maxwell’s electromagnetism equations and Hertz’s experiments on the generation and detection of electromagnetic waves in 1887 influenced the development of light’s wave nature. After the same time period. Several historical discoveries were made during the nineteenth century due to experimental studies on the conduction of electricity (Electrical discharge) through low-pressure gases in a discharge tube. The discovery of X-rays by Roentgen in 1895 and the electron by J. J. Thomson in 1897 was a watershed moment in science. Understanding of atomic structure It was discovered that at a sufficiently high level. At a low pressure of approximately 0.001 mm of the mercury column, a discharge occurred to apply an electric field to the gas between the two electrodes throughout the discharge tube.

A fluorescent glow appeared on the glass opposite the cathode. The type of glass determined the colour of the glass’s glow. It’s yellowish-green for soda glass. What is causing this fluorescence? Radiation that appeared to be emanating from the cathode was blamed. In 1870, William Thomson discovered cathode rays. Crookes, a physicist from the United Kingdom, later proposed in 1879 that these rays were streams of negatively charged particles moving quickly. J. J. Thomson confirmed this hypothesis (1856-1940).

THE PHOTOELECTRIC EFFECT AND LIGHTWAVE THEORY

By the end of the nineteenth century, the wave nature of light and the de Broglie Wavelength of an Electron had been well established. The lightwave model naturally and satisfactorily explained interference, diffraction, and polarisation.

According to this model, light is an electromagnetic wave composed of electric and magnetic fields, with a continuous distribution of energy over the region of space that the wave extends. Let us now see how this wave of light can explain the photoelectric emission observations from the previous section.

According to the wave picture of light, the free electrons on the surface of the metal (across which the beam of radiation falls) continuously absorb the radiant energy. The amplitude of electric and magnetic fields increases as radiation intensity increases. As a result, the greater the intensity, the more energy each electron should absorb.

The maximum kinetic energy of the photoelectrons on the surface is expected to increase as the intensity increases in this illustration. Moreover, irrespective of radioactivity frequency, an intense enough beam of radiation (for a long enough time) should impart enough energy to electron density to surpass the least energy needed to break free from the surface of the metal.

As a result, there should be no such thing as a threshold frequency.

Furthermore, the absorption of energy by electrons occurs continuously across the entire wavefront of the radiation in the wave picture. Because many electrons absorb energy, the amount of energy absorbed per electron per unit time is small.

According to explicit calculations, a single electron can take hours or more to accumulate enough energy to overcome the work function and exit the metal.

De Broglie’s Wavelength

In 1923, Prince Louis-Victor de Broglie (1892–1987), a French physics grad student, decided to make a drastic plan to advance the optimism that nature is symmetric. If matter possesses both particle and wave properties, and EM radiation possesses both particle and wave properties, nature would be symmetric.

If we once thought an unambiguous wave (EM radiation) is indeed a particle, then what we once thought was an unambiguous particle (matter) could also be a wave. The suggestion made by De Broglie as part of this research thesis was met with the same scepticism. When Einstein received a copy of his thesis, he stated that it was not only likely correct but could be of crucial importance. Einstein and a few other notable physicists helped De Broglie obtain his doctorate.

de Broglie Wavelength formula used both relativity and quantum mechanics to develop his proposal that all particles have a wavelength, which is given by

λ= h/ p

Where h denotes Planck’s constant and p denotes momentum. This is known as the de Broglie wavelength. (Note that this is already true for photons based on the equation.)

Interference is the distinguishing feature of a wave. If the matter is a wave, it must interact in constructive and destructive ways. Why isn’t this more commonly observed? The answer is that a wave must interact with an object about the same size as its wavelength to produce significant interference effects. Because h is so small, it is also very small, especially for macroscopic objects. For example, a 3 kg bowling ball moving at 10 m/s has

λ = h/p

λ = 6.63×10−34 J ⋅ s/(3 kg)(10 m/s)

λ = 2×10−35 m

This implies that the ping pong ball had to contact something 10−35 m in size to see its ripple qualities, which is far narrower than anything previously observed. When waves interact with objects with wavelengths many times their own, the intervention impacts are marginal, and the ripples start moving in parallel lines (such as light rays in geometric optics). The lengthiest wavelength for easily observed interaction forces from matter particles, so the littlest material possible, would be advantageous. Consequently, electrons were used for the first time to observe this effect.

In conclusion:

American theoretical physicist Clinton J. Davisson and Lester H. Germer discovered diffraction patterns in 1925, and British physicist G. P. Thomson (son of J. J. Thomson, the discoverer of the electron) discovered diffraction patterns in 1926. These trends are exactly consistent with electron interference with the de Broglie wavelength and are similar to illumination interacting with a diffraction grating.