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

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SUMMARY

The wavelength of an electron moving at 1 m/s is calculated using De Broglie's equation, λ = h/p, where h is Planck's constant (6.626 069 57 x 10^-34) and p is momentum. The momentum is determined by multiplying the mass of the electron (9.109 382 91 x 10^-31 kg) by its velocity (1 m/s), resulting in a momentum of 9.109 382 91 x 10^-31 kg·m/s. The final wavelength calculation yields λ = 0.727 389 51 x 10^-3 meters, confirming the correct application of the formula and calculations.

PREREQUISITES
  • Understanding of De Broglie's equation for wavelength calculation
  • Knowledge of momentum calculation (P = mass * velocity)
  • Familiarity with Planck's constant and its significance in quantum mechanics
  • Basic arithmetic operations involving scientific notation
NEXT STEPS
  • Study advanced applications of De Broglie's equation in quantum mechanics
  • Explore the implications of wave-particle duality in electron behavior
  • Learn about the significance of Planck's constant in various physical phenomena
  • Investigate the relationship between velocity and wavelength in different particles
USEFUL FOR

Students in physics, particularly those studying quantum mechanics, as well as educators and anyone interested in the wave properties of particles like electrons.

AdrianHudson
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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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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 ?
 
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:
AdrianHudson said:
Oh crap ! MY bad human error it is a typo!

Thought so! But instructors mark off for those too! :smile:
 
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
 

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