De Broglie Wavelength Calculation for an Electron with KE= 8.5 eV

In summary, the homework statement is asking what the de Brolie wavelength of an electron is with KE=8.5 eV. The Attempt at a Solution tried to solve for v and got 1.3617e-18 joules. This was then used to solve for p and got 9.11e-31 joules. Finally, p was used to get λ which was found to be 4.209e-10 picometers.
  • #1
starthorn
7
0

Homework Statement


What is the De Broglie wavelength of an electron with KE= 8.5 eV?


Homework Equations


λ=h/p
KE=0.5mv2
p=mv


The Attempt at a Solution


I converted 8.5 eV into joules:
8/5 eV × 1.602e-19 J = 1.3617e-18

Then used it for KE to solve for v:
I got 1729006.11

Used v to get p:
9.11e-31 × 1729006.11 = 1.575e-24

Used p to get λ:
6.63e-34/1.575e-24

And received λ= 4.209e-10

The answer required is on the order of picometers, and when I convert it to pm the answer is wrong. Entering it as it is also comes up wrong.
Sorry I use excessive sigfigs, my homework is through the Connect system for my textbook and there is a VERY SMALL margin of error so you always have to keep a bunch of extra or the answer might come up as wrong if you round too early.
 
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  • #2
You might need to use the relativistic momentum:
p=γm0v
(γ is the lorentz factor)
 
  • #3
starthorn said:
What is the De Broglie wavelength of an electron with KE= 8.5 eV?

Are you sure it's not KE = 8.5 keV? Your calculations look OK.

The answer required is on the order of picometers

What is it?

Sorry I use excessive sigfigs,

Ideally you should not round at all until you reach the final answer, i.e. keep the intermediate numbers in your calculator as you go along. Or better yet, derive an equation that let's you plug in your given numbers and get the final answer immediately. But I don't think that's your problem.
 
  • #4
Nessdude14 said:
You might need to use the relativistic momentum:
p=γm0v
(γ is the lorentz factor)
The hint portion of the problem states that it is not relativistic but I will check my calculations with it. Seeing as how the velocity I calculated is slightly under 0.006c though I am sure it is not.

jtbell said:
Are you sure it's not KE = 8.5 keV? Your calculations look OK.

Part a is in eV and part b is in keV, so yes I am sure


jtbell said:
What is it?
I can't see the answer without "giving up" on the problem, which means I will lose the credit for it. I know, it is an awful faulty system, but what can I do? It's the one my professor uses.
 
  • #5
It's definitely not relativistic, as stated. 8.5 eV << 511 keV (the rest-energy of an electron).

Either you're missing something in the problem statement, or the answer in the "system" is simply wrong. Textbooks do sometimes have a wrong answer for a problem.

I tried using different units for the intermediate steps and I still get the same answer.
 

Related to De Broglie Wavelength Calculation for an Electron with KE= 8.5 eV

1. What is the De Broglie wavelength and how is it related to kinetic energy?

The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle in motion. It is directly related to the particle's kinetic energy, with a higher kinetic energy resulting in a shorter De Broglie wavelength. This relationship is mathematically represented by the equation λ = h/mv, where λ is the De Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.

2. How does the concept of wave-particle duality apply to the De Broglie wavelength?

The concept of wave-particle duality states that particles can exhibit both wave-like and particle-like properties. This applies to the De Broglie wavelength because it describes the wave-like behavior of particles in motion, while also considering their particle-like characteristics, such as mass and velocity.

3. Can the De Broglie wavelength be measured experimentally?

Yes, the De Broglie wavelength has been experimentally observed in various experiments, such as the famous double-slit experiment, where the wave-like behavior of particles was demonstrated. Additionally, the De Broglie wavelength has been used to explain the diffraction patterns observed in electron microscopy.

4. How does the De Broglie wavelength relate to the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to precisely know both the position and momentum of a particle simultaneously. The De Broglie wavelength is related to this principle because it describes the momentum of a particle in motion, which is inherently uncertain according to the principle.

5. What are the practical applications of understanding the De Broglie wavelength from kinetic energy?

The understanding of the De Broglie wavelength from kinetic energy is crucial in various fields, such as quantum mechanics, particle physics, and even in everyday technology, such as electron microscopy and laser technology. It also helps us to better understand the behavior of particles at the atomic and subatomic level, leading to advancements in fields such as material science and nanotechnology.

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