Question

Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nanometers) of such a proton moving at $2.90 \times 10^{8} \mathrm{~m} / \mathrm{s}$ (mass of a proton $=1.673 \times$ $\left.10^{-27} \mathrm{~kg}\right)$

Name: Problem 58, Chapter 3: Chemistry: Atoms First
Uploaded: 2022-03-23T01:57:32-08:00
Duration: 2 min 21 s
Channel: Susan Hallstrom
Description: Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nanometers) of such a proton moving at 2.90 ×10^8 m / s (mass of a proton =1.673 ×.10^-27 kg)

   Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nanometers) of such a proton moving at $2.90 \times 10^{8} \mathrm{~m} / \mathrm{s}$ (mass of a proton $=1.673 \times$ $\left.10^{-27} \mathrm{~kg}\right)$

Chemistry: Atoms First

Julia Burdae, Jason… 3rd Edition

Chapter 3, Problem 58

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Solved by Expert Susan Hallstrom

03/23/2022

Step 1

90 \times 10^{8} \mathrm{~m/s}$ and the mass of the proton $m = 1.673 \times 10^{-27} \mathrm{~kg}$. We also know the Planck's constant $h = 6.626 \times 10^{-34} \mathrm{~m^2 kg / s}$. Show more…

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Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nanometers) of such a proton moving at $2.90 \times 10^{8} \mathrm{~m} / \mathrm{s}$ (mass of a proton $=1.673 \times$ $\left.10^{-27} \mathrm{~kg}\right)$

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Key Concepts

De Broglie Wavelength

This concept states that any moving particle has an associated wavelength, given by the relation ? = h/p, where h is Planck's constant and p is the momentum of the particle. It is a fundamental idea underlying matter-wave duality in quantum mechanics, linking the particle and wave natures of matter.

Momentum

Momentum, defined as the product of mass and velocity, is a crucial physical quantity in both classical and quantum mechanics. In the context of de Broglie’s hypothesis, a particle's momentum determines its associated wavelength, illustrating the inverse relationship between speed (or mass) and wave character.

Unit Conversion

Unit conversion, such as converting meters to nanometers, is an essential skill in physics that ensures the final answer is expressed in the appropriate or requested units. It bridges the gap between raw calculational results and their practical, understandable forms.

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