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Questions and Answers
What is the wavelength in nanometers of a quantum of light with a frequency of $8 \times 10^{15}$ s$^{-1}$?
The wavelength is approximately 3.75 × 10$^{-8}$ m or 37.5 nm.
Calculate the de Broglie wavelength of a 1000 kg car moving at 36 km/hr.
The de Broglie wavelength is approximately 6.626 × 10$^{-38}$ m.
State the formula associated with the Heisenberg uncertainty principle.
The formula is Δx Δp ≥ h/4π.
To which objects does Heisenberg's uncertainty principle apply?
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If the position of an electron is measured to 1.0 nm, what is the minimum uncertainty in the momentum of a helium atom?
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What is the uncertainty in the position of an electron with a mass of 9.1 × 10$^{-31}$ kg moving at 300 m/s if the accuracy is 0.001%?
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What is the significance of the Heisenberg uncertainty principle for objects of various masses?
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Which quantum number determines the orientation of an atomic orbital?
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Study Notes
Planck's Constant and Wavelength
- The value of Planck's constant is 6.63 x 10^-34 Js.
- The velocity of light is 3.0 x 10^8 m/s.
- The wavelength of a quantum of light is related to its frequency by the equation: wavelength = speed of light / frequency.
de Broglie Wavelength
- The de Broglie wavelength of a particle is related to its momentum (mass * velocity) by the equation: wavelength = Planck's constant / momentum.
Heisenberg Uncertainty Principle
- The Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty.
- Mathematically, the uncertainty principle is expressed as: Δx Δp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant.
Uncertainty Principle Application
- The uncertainty principle applies to all moving objects, not just atoms, electrons, or nuclei.
Quantum Numbers
- The orientation of an atomic orbital is determined by the magnetic quantum number (ml).
- The principal quantum number (n) indicates the energy level of an electron.
- The azimuthal quantum number (l) describes the shape of an electron orbital.
- The spin quantum number (ms) describes the intrinsic angular momentum of an electron, which is quantized and can be either spin up (+1/2) or spin down (-1/2).
Electron Energy Levels
- Electrons with higher principal quantum numbers (n) have higher energy levels.
- For a given principal quantum number, electrons with higher azimuthal quantum numbers (l) have higher energy levels.
- The set of quantum numbers (n, l, ml, ms) determines the specific state and energy of an electron in an atom.
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Description
Test your understanding of key concepts in quantum mechanics including Planck's constant, the de Broglie wavelength, and the Heisenberg uncertainty principle. This quiz covers essential equations and applications relevant to quantum behavior of particles.
