9. Quantum Mechanics

De Broglie Wavelength

Deriving The De Broglie Wavelength

deBroglie Wavelength Calculation Example (velocity given wavelength)

The smallest atoms can themselves exhibit quantum-mechanical
behavior. Calculate the de Broglie wavelength (in pm) of a
hydrogen atom traveling at 475 m/s.

A proton in a linear accelerator has a de Broglie wavelength of 
122 pm. What is the speed of the proton?

Use the de Broglie relationship to determine the wavelengths
of the following objects: (a) an 85-kg person skiing at
50 km/hr

Consider an atom traveling at 1% the speed of light. The de Broglie wavelength is found to be 7.1316 x 10-39 m. Which element is this?

At what speed in meters per second must a 145 g baseball be traveling to have a de Broglie wavelength of 0.500 nm?

De Broglie Wavelength Problems In Chemistry

Neutron diffraction is an important technique for determining 
the structures of molecules. Calculate the velocity of a 
neutron needed to achieve a wavelength of 125 pm. (Refer to 
the inside cover for the mass of the neutron.)

The faster an electron is moving, the _________ its kinetic energy, and the __________ its wavelength.

A 0.22-caliber handgun fires a 1.9-g bullet at a velocity of 765 m>s. 
Calculate the de Broglie wavelength of the bullet. Is the wave nature 
of matter significant for bullets?

Physics - Modern Physics (11 of 26) The de Broglie Wavelength

(c) What is the velocity of an electron with a de Broglie wavelength equal to (b)?

The resolution limit of a microscope is roughly equal to the
wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce
much higher resolution images, about 0.20 nm in modern instruments.
Assuming that the resolution of an electron microscope
is equal to the de Broglie wavelength of the electrons
used, to what speed must the electrons be accelerated to obtain
a resolution of 0.20 nm?

X rays with a wavelength of 1.54 * 10-10 m are produced when a copper metal target is bombarded with high-energy electrons that have been accelerated by a voltage difference of 30,000 V. The kinetic energy of the electrons equals the product of the voltage difference and the electronic charge in coulombs, where 1 volt-coulomb = 1 J.
(a) What is the kinetic energy in joules and the de Broglie wavelength in meters of an electron that has been accel-erated by a voltage difference of 30,000 V?

What velocity would an electron (mass = 9.11 * 10-31 kg) need for its de Broglie wavelength to be that of red light (750 nm)?

(b) Light with a wavelength of 2.50 * 10-7 m falls on a piece of chromium in an evacuated glass tube. What is the minimum de Broglie wavelength of the emitted elec-trons? (Note that the energy of the incident light must be conserved; that is, the photon’s energy must equal the sum of the energy needed to eject the electron plus the kinetic energy of the electron.)

Protons and electrons can be given very high energies in particle accelerators. What is the wavelength in meters of an electron (mass = 9.11 * 10-31 kg) that has been accelerated to 5% of the speed of light? In what region of the electromagnetic spectrum is this wavelength?

De Broglie Wavelength Example 1

Among the elementary subatomic particles of physics is the
muon, which decays within a few microseconds after formation.
The muon has a rest mass 206.8 times that of an electron.
Calculate the de Broglie wavelength associated with a
muon traveling at 8.85 * 105 cm/s.

The de Broglie Wavelength and Wave Particle Duality - A Level Physics

The de Broglie Wavelength

What is the de Broglie wavelength in meters of a baseball weighing 145 g and traveling at 156km/h? Why do we not observe this wavelength?

De-Broglie Wavelength of a Quantum Particle.

Calculate the de Broglie wavelength of a 143-g baseball traveling
at 95 mph. Why is the wave nature of matter not important for
a baseball?

Use the de Broglie relationship to determine the wavelengths
of the following objects: (d) an ozone 1O32 molecule
in the upper atmosphere moving at 550 m/s.

The speed of sound in dry air at 20 °C is 343 m/s and the lowest
frequency sound wave that the human ear can detect is approximately 20 Hz. (b) What would be the frequency of electromagnetic radiation with the same wavelength?

What is the velocity (in m/s) of an electron that has a wavelength of 3.13 x 105 pm? (Mass of an electron = 9.11 x 10-31 kg).

The first 25 years of the twentieth century were momentous 
for the rapid pace of change in scientists’ understanding 
of the nature of matter. (b) In what ways is de Broglie’s hypothesis, as it applies to 
electrons, consistent with J. J. Thomson’s conclusion that 
the electron has mass? In what sense is it consistent with 
proposals preceding Thomson’s work that the cathode rays 
are a wave phenomenon?

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[BOOK CHEM] Clutch Version

Wavelength and Frequency

Wavelength&nbsp;is the distance from one crest of a wave to another, whereas frequency is the number of waves within a second.&nbsp;

Quantum Numbers: Spin Quantum Number

The Spin Quantum Number deals with the spin of an electron within an orbital.

Speed of Light

The Speed of Light in a vacuum is related to the wavelength and frequency of a light particle.

Bohr Equation

In the Bohr Equation, the energy and wavelength a photon is related to its energy shell transitions.

Quantum Numbers: Angular Momentum Quantum Number

The&nbsp;Angular Momentum Quantum Number&nbsp;gives the shape of the atomic orbitals.

Emission Spectrum

Emission Spectra is a series of lines formed when emitted light is focused by a slit and passed through a prism. &nbsp;

Introduction to Quantum Mechanics

The 4 Quantum Numbers provide us the coordinates to find the theoretical location of an electron.

Quantum Numbers: Nodes

A node is the region in an atom with zero electron density and where an electron is least likely to exist.

The Energy of Light

The Energy of Light&nbsp;involves the use of a new variable Planck's Constant.

Electromagnetic Spectrum

The Electromagnetic Spectrum is the different forms of radioactive energy that exists in our universe.

Heisenberg Uncertainty Principle

Heisenberg's Uncertainty Principle&nbsp;tries to explain the potential duality of an electron behaving as either a particle or wave.&nbsp;

Quantum Numbers: Number of Electrons

The Quantum Numbers can give both the quantity and location of electrons within a given atom.&nbsp;

Quantum Numbers: Principal Quantum Number

The Principal Quantum Number gives both the size and energy of an electron shell.&nbsp;

Photoelectric Effect

What happens when light strikes the surface of a metal? The Photoelectric Effect&nbsp;can help to explain that.&nbsp;

Quantum Numbers: Magnetic Quantum Number

The Magnetic Quantum Number gives the location of an electron within a specific orbital.

Bohr Model

In the Bohr Model, electrons can move up and down to different orbitals or shells based on absorbing or releasing of energy.&nbsp;

The&nbsp;De Broglie Wavelength equation relates wavelength to velocity or speed.&nbsp;

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