About a hundred years ago, Louis de Broglie proposed that matter that was moving…
CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom
Problem
About a hundred years ago, Louis de Broglie proposed that matter that was moving would exhibit wave-like properties.
For this question, consider some particles, each of mass m, moving with a speed v, towards a barrier in which there is a small hole about the same size (or just a little larger) as the particles.
(1) How much momentum would a particle have?
(2) Many of the particles arriving at the barrier will be stopped as they collide with (and perhaps bounce off) the barrier. But some of the particles will pass through the hole—and when they do their paths will change a little, causing them to spread out as they move beyond the hole.
- i What wave property is the spreading out of the paths of the particles mimicking?
- ii If the particles had more momentum (perhaps because they move faster), would you expect them to spread out more, or less, as they pass through the hole? Justify your answer.
- iii If the hole in the barrier were made very much larger, (say, more than 10 times the size of the particles) would you expect the spreading out of the particles to be more, or less, than before? Justify your answer.
(3) So, if the particles show behaviour similar to that of waves, we can assign them a wavelength, λ.
- i With reference to your answer from part b ii, suggest how the wavelength of a moving particle is related to its momentum.
- ii With reference to your answer to part b iii, suggest how the amount of spreading out of the paths of the particles is related to the momenta of the particles and to the size of the hole.
(4) Which of the following particles would you expect to show the greatest amount of wave behaviour? Justify your answer.
- a fast-moving proton
- a stationary atomic nucleus
- a slow-moving electron
(5) The time-dependent wave function, describing any particle, developed by Erwin Schrödinger can be manipulated to form a probability density function. What does this function tell us about the particle?