# Calculating De Broglie Wavelength from Kinetic Energy

• jinksys
In summary, the De Broglie wavelength equation, λ = h/mv, shows the relationship between the wavelength of a particle and its kinetic energy. To calculate the De Broglie wavelength from kinetic energy, use the equation λ = h/√(2mK), which takes into account the uncertainty of the particle's velocity. This concept can be applied to all particles, but is most commonly used for those with small masses, such as electrons. The De Broglie wavelength is important in quantum mechanics as it helps to explain the behavior of particles at the atomic level and the wave-like nature of matter.
jinksys

## Homework Statement

Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is given by

$$\lambda = \frac{hc}{\sqrt{KE(KE + 2mc^2)}}$$

## The Attempt at a Solution

I know:

$$KE = {\gamma}mc^2 - mc^2 = pc - mc^2$$

But from here I am lost. I have a hunch that I need to use the equation that equates Energy and Momentum, but I'm lost.

Last edited:
The problem is that your equation only applies to the relativistic limit, in general
$$E_k = \sqrt{(pc)^2 + (mc^2)^2} - mc^2$$
Try using that.

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

The De Broglie wavelength equation is λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity. This equation shows the relationship between the wavelength of a particle and its kinetic energy, where a higher kinetic energy results in a shorter wavelength.

## 2. How do you calculate the De Broglie wavelength from kinetic energy?

To calculate the De Broglie wavelength from kinetic energy, use the equation λ = h/√(2mK), where K is the kinetic energy of the particle. This equation takes into account the fact that the particle's velocity may not be known, so the kinetic energy is used instead.

## 3. Can the De Broglie wavelength be applied to all particles?

Yes, the De Broglie wavelength equation can be applied to all particles, including electrons, protons, and even larger objects like atoms and molecules. However, it is most commonly used for particles with very small masses, such as electrons.

## 4. How does the De Broglie wavelength relate to the wave-particle duality of matter?

The De Broglie wavelength is a key concept in the wave-particle duality of matter, which states that particles can exhibit both wave-like and particle-like behavior. This means that particles, such as electrons, can have both a wavelength and a mass, and can behave like waves in certain situations.

## 5. Why is the De Broglie wavelength important in quantum mechanics?

The De Broglie wavelength is important in quantum mechanics because it helps to explain the behavior of particles at the atomic and subatomic level. It also provides a way to describe the wave-like behavior of matter, which is crucial in understanding phenomena such as electron diffraction and the behavior of particles in quantum systems.

Replies
5
Views
2K
Replies
2
Views
5K
Replies
7
Views
2K
Replies
2
Views
7K
Replies
2
Views
1K
Replies
1
Views
3K
Replies
4
Views
4K
Replies
4
Views
3K
Replies
27
Views
1K
Replies
3
Views
2K