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12 Dec 2019

What two concepts underpin Schrodingerâs equations for the energies of electrons in an atom:

Standing waves are quantized and of fixed energy

Conservation of energy and wave-particle duality

Uncertainty principle and wave-particle duality

Opposite charges attract and the uncertainty principle

Frequency and wavelength of wave motion are related to velocity.

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Jean KeelingLv2

13 Dec 2019

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Just as light waves have particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher its kinetic energy and the shorter its wavelength. The wavelength, Î», of a particle of mass m, and moving at velocity v, is given by the de Broglie relation

Î»=hmv

where h=6.626Ã10â34 Jâ s is Planck's constant.

This formula applies to all objects, regardless of size, but the de Broglie wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave properties. In contrast, the wave properties of subatomic particles can be seen in such experiments as diffraction of electrons by a metal crystal.

Part A

The mass of an electron is 9.11Ã10â31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31Ã10â10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00Ã108 m/s.

Express your answer numerically as a percent.

Part B

The mass of a golf ball is 45.9 g . If it leaves the tee with a speed of 60.0 m/s , what is its corresponding wavelength?

what is the final state energy level in H atom transition, if the electron starts from n=2 and the atom absorbs a photon with frequancy 4.57x10^14 Hz ?

CHEM 1430 LIGHT LAB SPRING 2018 A Danish physicist, Neils Bohr, a post-doctoral student in J. J. Thomson's lab and friend of Rutherford, took up the problem of electron arrangement within the atom. Bohr's breakthrough was recognizing Balmer's fixed emission wavelengths, when taken with Planck's Relationship, led to the conclusion the shells, like the radiation emitted, must be quantized (have set, specific energles). Bohr proposed the electrons circulated about the madeus, much like planets cirde surãin seres of concentric shells of increasing size. Each shell stood at a fixed (set) distance from the nucleus with the shell nearest the nucleus taking the m and a shell further away taking the n in the B-R equation. The integral values of m and n taken with the discrete wavelength led Bohr to propose the shells were "quantized," meaning electrons could only exist at the surface of the shells. When an electron moved from a high shell, n, to a low shell, m, light of a foxed wavelength was emitted Bohr reasoned the shells were special due to this quantized nature. An electron in a shell occupied what Bohr described as a "steady state," meaning the electron could circulate about the nucleus without loss or gain of energy. This steady state proposition, which conflicted with classical physics, could not be explained by then available data but was required for Bohr's proposed structure to be stable. Later work revealed the wave-particle duality of the electron which lead to acceptance of the Steady State Proposition. The energy of an electron in any shell, represented by n, can be calculated using an equation derived from combining the Balmer-Rydberg and Planck equations. The energy of an electron in the no shell is given by é¦¯.h RL where hcR,-2.18x10-*) where Ru, is the Rydberg's Constant for the hydrogen atom, h is Planck's Constant and c is the speed of light NOTE: The energy is given a nexative value to refect the stabillting, attractive force between the negatively charged electron and the positively charged nucleus. As the shell number n increases, the attractive force decreases leading to a rising shell energies (E, increases, values less negative). ACTIVITY Calculate the energles for an electron in the first 7 shells of the hydrogen atom using the above relationship, recording the values in the center column of the Hydrogen the right-hand column in the table, convert the shell with the exponent of 10 Improper sclentific notation is typically used to plot data covering several orders of magnitude (powers of ten). Shell Energy Table. For energies to improper scientific notation Hydrogen Shell Energy Table Shell Value, n Calculated Shell Energy.ã Express Shell Energy in improper Scientific Notation, x 10-1 Page 9 of 12

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		Standing waves are quantized and of fixed energy
		Conservation of energy and wave-particle duality
		Uncertainty principle and wave-particle duality
		Opposite charges attract and the uncertainty principle
		Frequency and wavelength of wave motion are related to velocity.