Quantum Mechanics Flashcards
When energy is shown through a prism, visible light is diffracted into a spectrum of light whereas if energy is funneled through a tube filled with hydrogen gas, certain colors are only emitted at different energy levels. Compare and contrast the different terminologies.
The diffraction gradient by a prism is called the continuous spectrum where all the colors of light are lined side by side. Whereas different color lights emitted by the same molecule is called a line spectra.
True or False: Line spectrums are unique to different atoms of the same element.
False. The line spectra of the same element are the same, whereas the line spectrums are unique to elements
This equation, 1/λ = R (1/J^2 - 1/I^2) is to calculate the wavelength when:
A. When a photon is traveling to an electron
B. When a photon is absorbed by an electron
C. When a prism diffracts visible light into different colors
D. When a photon is released by an electron
1/λ = R (1/J^2 - 1/I^2) is used to calculate the wavelength of a photon released by an electron as it emits the energy
The Rydberg constant used to determine wavelengths:
A. 1.097 e-6/m
B. 1.097 e-7/m
C. 1.097 e6/m
D. 1.097 e7/m
D. 1.097e7/m
What color light is released when an electron of a hydrogen atom falls from n=4 to n=2?
1/λ = R (1/J^2 - 1/I^2) 1/λ = 1.1e7/m (1/4^2 - 1/2^2) 1/λ = 1.1e7/m (1/16 - 1/4) 1/λ = 1.1e7/m |(-0.19)| 1/λ = 0.206e7=> λ = 4.85e7 => 485 nm [BLUE!!!]
What is the wavelength of the light when an electron of a hydrogen falls from n=5 to n=2
1/λ = R (1/J^2 - 1/I^2) 1/λ = 1.09e7/m (1/5^2 - 1/2^2) 1/λ = R (1/25 - 1/4) 1/λ = 1.09e7/m |(-0.21)| 1/λ = 0.2289 e7/m λ = 4.36e7m => 436 nm
What is the line spectra of hydrogen often called?
Balmer Series. It is called Balmer, because it utilizes the Balmer Rydberg constant and equation to find out about the wavelengths
In an experiment, you are determining the line spectra of different elements. One unknown element releases a photon with a wavelength of 120 nm. Can you use the Balmer series to determine the color of the wave?
While you can use the Balmer Rydberg equation to calculate the wavelength of the photon released, you are unable to use the series to identify the color of the wave. This wavelength is beyond the sight of humans and falls into the UV spectra.
Which principle entails the inability to understand both momentum and the position of an electron precisely at the same time? A. Coulomb’s Law B. Heisenberg Principle C. Balmer - Rydberg D. Planck’s Law
B. Heisenberg Uncertainty Principle. This principle states that one is unable to understand both physical quantities when dealing with subatomic particles
Describe the mathematical relationship of Heisenberg Uncertainty Principle.
(The uncertainty of position)(the uncertainty of momentum) = planck’s constant/pie*constat. [Note: The constant is dependent on the textbook. Different books have different values and it can ultimately lead to different values]
True or False: In the equation: ΔxΔρ = ℏ/2π, Δ represent the changes in the position (x) and the momentum of the object of interest (ρ)
False. The Δ are the respective uncertainties of the particle’s position and momentum and h is Planck’s constant not the change of the two variables. These Δ are not the expected values as depicted from the Bohr model.
According to the Heisenberg principle, as you decrease the uncertainty of position, therefore understand the precision of where your particle’s position is, what should be occurring? A. Increase in Planck’s Constant B. Decrease in particle’s momentum C. Increase in particle’s momentum D. Decrease in constant before pi
C. Increase in particle’s momentum. In order to understand the precision of the particle’s position, the particle’s momentum increases, because there is no possible way to understand both the position and momentum of a subatomic particle precisely.
If an electron traveling in a counterclockwise fashion has a 10% uncertainty in its velocity of 2.2e-6, what is the momentum of its travel?
momentum = mv(.1) => 9e-312.2e-60.1 = 2e-25 (the uncertainty in the momentum is 2.0e-25 kgm/s)
[Note: mass of an electron is 9e-31]
Compare the position of the electron with a 10% uncertainty with diameter of radius
The bohr model predicts the radius of the first electron cloud from the nucleus to be 5.11 e-11m
Plugging in this value into the uncertainty principle
Diameter of the shell is 2r_1 =
2(5.3e-11) = 1.06e-10m
Our uncertainty of the position of the electron in orbit is greater than the diameter itself.
Therefore the Bohr model is wrong!!! The model is tell us that the electron is orbiting at a certain speed at a radius from the center, but based on calculations, this radius is not as the bohr model has predicted
Why have the bohr model if it is wrong?
It is useful for beginning to learn chemistry
Much of the uncertainty principle goes against our ration. Without the principle, the numbers are pretty accurate. These things are not noticeable on a macroscopic level. But microscopically, it becomes important to
Why is the idea of uncertainty principle and concept hard to grasp?
In quantum mechanics, the wave-particle duality of electrons does not allow us to accurately calculate both the momentum and position because the wave is not in one exact location but is spread out over space. In classical physics, these two properties are possible to define at once as these are discussing macroscopic concepts
When studying quantum mechanics, what must you understand in regards to the values of the measurements? What does this give way too?
Measurements dealing with Quantum mechanics there are always some levels of uncertainty. A limit to how precise these measurements can be made. This idea gives way to the Heisenberg Uncertainty - a result of wave particles duality of matter that exists at the subatomic level and atomic level. This principle has nothing to do with device or instrument to obtain the physical quantities of quantum mechanics. This is an inherent property of natural and comes from the fact that matter on a subatomic level can act as a wave AND a particle
In a thought experiment, you are attempting to understand how the energy of a light and wavelength are related to one another. Therefore you shine a light onto the a surface and slowly decrease the wavelength. What are your expected results. Why?
As we decreased the wavelength of the light used by the microscope, we increase the energy carried and the momentum carried by the photon of light
Given by Momentum of the photon of light from the microscope = speed of light/wavelength
Rho = c/lambda [ρ = c/λ]
Based on the equation, ρ = c/λ, what has to be done to increase the precise measurement of momentum of a photon.
Because C is constant we have to decreases the wavelength of light
This increases the momentum of the photon
As you are observing a sample through a microscope, how are you able to see the light through the lens? Describe the light travel.
Light from the source interacts with our sample’s electrons. [This interaction of a photon and electrons causes the electron to gain velocity] After this, it is deflected off the sample and travels through the lens to reach our eyes.
As a review, how does the wavelength of a photon affect the momentum of an electron it interacts with?
The lower the wavelength, the higher the momentum of the electron. Therefore!! The higher the velocity (deceiving)
Heisenberg’s Uncertainty Principle entails what about the collision of a photon and electron if the position of the collision is known?
The momentum of the collision will be unknown if the position is known. According to the principle, it is impossible to know both the position and momentum/velocity of a microscopic quantity. [ (Δx)(Δρ) ≥ h = h/2π OR h/Δρ]
What is the mathematical representation of heisenberg uncertainty principle?
(Δx)(Δρ) ≥ h = h/2π
H bar - a constant h/2pie = 1.05e-34J/sec
Delta x - change in position
Delta p - Change in momentum
This tells us that the more precise the position of the particle, the smaller Δx will be and the larger the momentum (therefore the less we know about the momentum) and vice versa.
True or False: According to the Heisenberg Uncertainty Principle, we are unable to know the precision of both momentum and position simultaneously of a photon. Therefore we are unable to find the precise value of them.
False. We are still able to find the precise values of one of the two variables.
True of False: Heisenberg Uncertainty Principle stems from the limitations of measurement tools
False, These are due to the inherent property of nature and come from the fact that matter on a subatomic level can act as a wave AND a particle. It has nothing to do with the measurement tools we have on hand [but may change with technology]
True or False: According to the Heisenberg Uncertainty Principle, we are unable to know the precision of both momentum and position simultaneously of a photon. Therefore we are unable to find the precise value of them.
True. An electron is not actually a particle and the principle only works in calculating a particle that has both wave and particle characteristics. Therefore an electron can not have a precise momentum and a precise position!!!!
What is the uncertainty of an electron’s position if it was orbiting at 2 million meters per second and the precision of the velocity is 0.15%?
(Δx)(Δρ) ≥ h => Δx = h/Δρ => 1.055e-34 Js / (9.11e-31kg0.0015*2e6m/s)
= 3.86e-8m or 38.6 nm
By the uncertainty principle, The best simultaneous position during this velocity will have an uncertainty of 38.6nm along the electron’s plane of travel
Hesienberg’s Uncertainty Principle is dependent on Planck’s Constant (h): A. 1.055 e-34 m/s B. 1.055e-34 J*s C. 1.055 e 34m/s D. 1.055 3 34 J*s
B. 1.055e-34 J*s this number is the planck’s constant 6.6e-34/2π
The mass of an electron is A. 9.11 e34 g B. 9.11 e-34 g C. 8.5 e -34 g D. 9.11 e-31 g
B. 9.11 e-34 g is the same as 9.11e-31kg (this is the classically used value for the mass of electron)
Along with momentum and velocity, what physical quantities does the heisenberg uncertainty principle also include.
Just like how one is unable to find the momentum and position of a particle precisely (100%), you are also unable to find the exact time and energy of a particle as well. (Δt)(ΔE) ≥ h/2π => ΔE = h/2πΔt
An electron in n = 2 energy level of a hydrogen atom remains at this level for 80 nanoseconds before transitioning to a lower energy level given by n = 1. What is the uncertainty in energy released as the electron falls.
Heisenberg Uncertainty Principle. ΔE = h/Δt = 1.055e-34J*s / (80e-9 s) = 1.319 e-27 J
1.319 e-27 J is the uncertain energy in energy released as the electron jumps from n = 2 to n =1.
After working on a problem, you come to find that the uncertain energy released as an electron drops from n=2 to n=1 is 1.319 e-27 J. How much of this energy is the fraction of energy that the ΔE represents with respect to the total energy released by the transition of the electron?
S1: Rhydburg - This tells us the wavelength of the photon when it is released from the electron falling from n=2 to n=1 || 1/λ = R(1/n_1^2 - 1/n_2^2) = 1/λ = 1.097e7/m (1 - 4) = λ = 1.125 e-7m
S2: Find the energy of the photon || E = hc/λ = (6.26e-34 J*s)(3e8 m/s) / 1.215e-7m = 1.636e-18J
S3: Compare ΔE to the theoretical E = 1.319e-27 J/ 1.636e-18 J [the uncertainty of energy found here is 1 out of 1.24 billion!!!]
Upon calculating the uncertainties of a wheel moving on a car and an electron moving at the same speed, what should you expect when solving these problems? Why?
Because the macroscopic wheel has a larger mass, it will lead to uncertainty levels about its physical quantities very small, allowing us to neglect them in calculation. However, the electron’s mass is so small, this leads to a much bigger uncertainty level compared to big objects. Therefore we will have to consider the uncertainty of of microscopic objects
Uncertainty is used a lot in regards to chemists especially when it comes to quantum mechanics. What do they mean?
Chemists describe the estimated degree of error in a measurement as the uncertainty of the measurement
chem.libretexts.org
Contrast the classical mechanics from quantum mechanics in regards to the location of electrons.
Classical Mechanics embodies the Bohr model which states Electron in orbit around the nucleus in a specific pattern [classical mechanics, like planets orbit around the sun] - incorrect in electrons! Quantum Mechanics states that there is no way for knowing where the electron is 100% of the time but can say with high probability that the electron is in an orbital.
What is an orbital in quantum mechanics? How does it refer
is a region in space in which the electron is most likely to be found. Therefore for hydrogen, a sphere encompasses around the nucleus and in this region, we are likely to find the electron] The classical model states the electron is found at a at a distance
