Derive the infinite square well energy quantization using directly the de Broglie relation p=h/h by fitting an integral number of half de Broglie wavelengths /2 into the width of the well.
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- Use the uncertainty principle to show that if an electron were confined inside an atomic nucleus of diameter 2 x 10-15 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can be moving nonrelativistically.Calculate the frequency and momentum of a photon of wavelength 620 nm.A beam of electrons with kinetic energy 45 keV is shotthrough two narrow slits in a barrier. The slits are a distance 2.0 x 10-6 m apart. If a screen is placed 45.0 cm behind the barrier, calculate the spacing between the “bright” fringes of the interference pattern produced on the screen
- Electrons with a speed of 2.6 x 106 m/s pass through a double-slit apparatus. Interference fringes are detected with a fringe spacing of 5.8 mm. What will the fringe spacing be if the electrons are replaced by neutrons with the same speed? What speed must neutrons have to produce interference fringes with a fringe spacing of 5.8 mm?Please asapPls help ASAP
- The smallest atoms can themselves exhibit quantum mechanical behavior Calculate the de Broglie wavelength (in picometers) of a hydrogen atom traveling at 430 m/sm/s. Express your answer using three significant figures.An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).In the classical limit calculate the wavelength corresponding to an electron with the energy of 99 kev (kiloelectronvolt). Give your answer in Angstrom (10-10 1.6x10-10 m, then write 1.6 as your answer). This m, for example, if the answer is should give you a good idea why one can use a crystal lattice with an average interatomic distance of around 1010 m to observe electron diffraction.