What is the wavelength of an electron moving at 1 m/s?

In summary: You just need to round the answer to the correct number of significant figures. The answer should be 0.727 x 10^-3 meters.
  • #1
AdrianHudson
48
2

Homework Statement


What is the corresponding wavelength, in meters, of an electron moving at 1 m/s?
Velocity: 1 m/s
Planks Constant = 6.626 069 57 x 10^-34
Mass of electron = 9.109 382 91 x 10^-31
Momentum = unknown

Homework Equations


We need to find momentum to use De Broglie's equation.

Momentum = Mass * Velocity
De Broglie's Equation for finding the wavelength: λ = h/p
h being the Planck constant

The Attempt at a Solution



My attempt.

Finding momentum : P = 9.109 382 91 x 10^-31 * 1 m/s
p = 9.109 382 91 x 10^-31
finding the wavelength
First divide the numbers WITHOUT the exponent
so 6.626 069 57/9.109 382 91 = 0.727 389 51
now exponents -34/-31
= -3 (I took out the extra steps)

final answer λ = 0.727 389 51 x 10^-3

is this correct?
 
Last edited:
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  • #2
AdrianHudson said:
1. First divide the numbers WITHOUT the exponent
so 6.626 069 57/9.109 382 91 = 0.727 389 51
now exponents -34/-31
= -3 (I took out the extra steps)

final answer λ = .0727 389 51 x 10^-3

is this correct?


No.
How did you get from 0.727 389 51 to .0727 389 51 ?
 
  • #3
rude man said:
No.
How did you get from 0.727 389 51 to .0727 389 51 ?

Oh crap ! MY bad human error it is a typo!
 
Last edited:
  • #4
AdrianHudson said:
Oh crap ! MY bad human error it is a typo!

Thought so! But instructors mark off for those too! :smile:
 
  • #5
rude man said:
Thought so! But instructors mark off for those too! :smile:

Haha I will be more weary next time! So does the math look off? :-p
 
  • #6
Math is fine.
 

Related to What is the wavelength of an electron moving at 1 m/s?

What is the wavelength of an electron?

The wavelength of an electron refers to the distance between two consecutive crests or troughs in its wave pattern. It is a measure of the particle's energy and can be calculated using the de Broglie equation: λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is its velocity.

How is the wavelength of an electron related to its energy?

The wavelength of an electron is inversely proportional to its energy. This means that as the energy of an electron increases, its wavelength decreases. This relationship is described by the de Broglie equation, which shows that the wavelength is directly influenced by the electron's momentum and inversely influenced by its mass.

Can the wavelength of an electron be measured?

Yes, the wavelength of an electron can be measured experimentally using various techniques such as electron diffraction or electron microscopy. These methods involve the interaction of electrons with a material or a beam of light, which produces a diffraction pattern that can be used to determine the electron's wavelength.

What is the significance of the wavelength of an electron?

The wavelength of an electron is significant because it helps us understand the wave-particle duality of matter. It shows that even though electrons are considered as particles, they also exhibit wave-like properties. This concept has greatly contributed to our understanding of quantum mechanics and the behavior of particles at the atomic and subatomic level.

Does the wavelength of an electron change in different environments?

Yes, the wavelength of an electron can change in different environments, depending on its energy and the properties of the materials it interacts with. For example, in a vacuum, an electron's wavelength will remain constant, but in a material, it may change due to the electron's interaction with the atoms in the material. This phenomenon is known as electron scattering and is used in various applications, such as electron microscopy and spectroscopy.

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