# Crystal spacing of a solid surface, Bragg's law

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In summary, the conversation discusses a problem from a textbook involving a Low Energy Electron Diffraction (LEED) study of a solid surface. The goal is to calculate the crystal spacing d using Bragg's law and several equations, including nλ=2dsin(φ), λ=hc/E, and E=vh(n+1/2). The individual provides their attempted solution and expresses confusion about the values obtained, as well as the lack of an answer in the textbook.
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## Homework Statement

In a particular Low Energy Electron Diffraction (LEED) study of a solid surface, electrons at 45 eV were diffracted at $$\phi$$ = 53 degrees. Calculate the crystal spacing d.

## Homework Equations

n$$\lambda$$=2dsin($$\phi$$)
$$\lambda$$ = hc/E
wavelength = c/v
E = vh(n + 1/2)

Note here v is the frequency (nu looked weird on this site)

## The Attempt at a Solution

This questions comes from a problem in my textbook that was a recommended practice problem for an upcoming exam. Despite being an odd numbered problem the answer to it wasn't in the back of the book (figures). Anyways I just wanted to make sure I was solving it correctly.

Firstly I converted the 45 electronvolts into 7.209765E-18 Joules
Then by wavelength = hc/E, i found the wavelength to be 2.754E-8 Meters
Then I found the frequency to be 1.089324619E16 s-1
Next I found n to be 1/2 (which is weird cause I thought it would be an integer)
Lastly I plugged these values into bragg's law and got 8.623E-9 Meters

Like I said the answer was not in the book for some reason and I'd like to know if I'm doing this right

You need to show your steps better. Also, why are you using the last equation listed? That is for a quantum harmonic oscillator. In this case you just have diffraction.

## 1. What is Bragg's law?

Bragg's law is a scientific principle that explains the relationship between the spacing of crystal planes in a solid surface and the angle at which x-rays are diffracted.

## 2. How does Bragg's law relate to crystal spacing?

Bragg's law states that when x-rays are incident on a crystalline solid surface at a specific angle, they will be diffracted in a way that allows the measurement of the distance between adjacent crystal planes. This distance is known as the crystal spacing.

## 3. What is the significance of crystal spacing in solid surfaces?

The crystal spacing of a solid surface is important because it provides information about the arrangement of atoms within the crystal lattice. It also affects the physical and chemical properties of the solid.

## 4. Can Bragg's law be applied to all types of crystal structures?

Yes, Bragg's law can be applied to all types of crystal structures as long as they have regular and repeating arrangements of atoms. This includes ionic, metallic, and covalent crystals.

## 5. How is Bragg's law experimentally determined?

To determine the crystal spacing of a solid surface using Bragg's law, a beam of x-rays is directed at the surface at different angles. The intensity of the diffracted x-rays is then measured and used to calculate the crystal spacing using the equation nλ = 2dsinθ, where n is the order of diffraction, λ is the wavelength of the x-rays, d is the crystal spacing, and θ is the angle of diffraction.

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