# Quantum physics and wave lengths

In summary: But for a relativistic particle, \lambda = \frac{h}{\gamma m_0 v} Now the kinetic energy is K = (\gamma -1) m_0 c^2 The total energy is E = (\gamma m_0) c^2 So the kinetic energy is K = E - m_0 c^2 And the momentum is p = \sqrt{2m_0K} So the de Broglie wavelength is \lambda = \frac{h}{p} = \frac{h}{\sqrt{2m_0K}} Putting in the expressions for K and m_0, \lambda = \frac{hc

## Homework Statement

What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 1 MV ( you must use the relativistic mass and energy expressions at this high energy.)

ans. 8.7 x 10^-13

## Homework Equations

M= Mo/ square root (1 - v^2/c^2)

## The Attempt at a Solution

I have no idea where to go with this question i am completely stumped, can someone please steer me in some direction to understanding such and getting the right answer, thank you and i really appreciate it.

Last edited:
The question offers plenty of clues of where to start.

The desired answer is the de Broglie wavelength. Therefore, you could start at the end and work backwards. Do you know any equations for the de Broglie wavelength that might help you solve the problem? I know one that sticks out immediately; this equation relates the wavelength to only one other variable. Once you determine what this variable is, can you link it to the given data of the problem? If so, then problem solved.

well i assume now you use wavelength= h/mv and to find v i'd use Ee=Ek, just i need to find relativistic mass and energy first for the speed ill get is faster then that of light

Here is an important difference for the momentum: p = mv (non-relativistic), p = $$\gamma$$mv (relativistic).

De Broglie's original formula is

$$\lambda = \frac{h}{p}$$

## 1. What is quantum physics and how is it different from classical physics?

Quantum physics is the branch of physics that deals with the behavior of particles at the subatomic level. It differs from classical physics in that it describes the behavior of particles in terms of probabilities rather than definite values.

## 2. What is the concept of wave-particle duality in quantum physics?

Wave-particle duality is the idea that particles can exhibit both wave-like and particle-like behavior. This means that they can act as both a localized particle and a spread-out wave at the same time.

## 3. How are wave lengths related to quantum physics?

In quantum physics, particles are described as waves with a certain wavelength. This wavelength determines the energy and momentum of the particle.

## 4. What is the significance of Heisenberg's uncertainty principle in quantum physics?

Heisenberg's uncertainty principle states that it is impossible to know both the position and momentum of a particle simultaneously. This is because the act of measuring one property affects the other, making it impossible to have precise knowledge of both at the same time.

## 5. How is quantum entanglement related to wave lengths?

Quantum entanglement is a phenomenon in which two or more particles become connected in such a way that the state of one particle affects the state of the others, regardless of the distance between them. This connection is based on the particles' wave functions, which are described by their wave lengths.

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