# Distance between Isotopes in a mass spec

• Elvis 123456789
In summary, the problem involves finding the distance between the two adjacent lines formed by the three isotopes of krypton (82Kr, 84Kr, and 86Kr) on a photographic plate in a mass spectrometer. Given the electric and magnetic fields, the selected speed of the ions is found to be 2.83 * 10^4 m/s. The radius of each isotope is calculated to be 0.0360 m, 0.0369 m, and 0.0378 m, respectively. The question is asking for the distance between two adjacent impact locations on the particle detector target, which is found to be 2*[(Radius of 84Kr) - (Radius of 82Kr)].
Elvis 123456789

## Homework Statement

Suppose the electric field between the plates P and P' in the mass spectrometer in following figure is 1.89×104V/m and the magnetic field in both regions is 0.668 T.

If the source contains the three isotopes of krypton, 82Kr,84Kr, and 86Kr, and the ions are singly charged, find the distance between the two adjaicent lines formed by the three isotopes on the photographic plate. Assume the atomic masses of the isotopes (in atomic mass units) are equal to their mass numbers, 82, 84, and 86. (One atomic mass unit = 1u = 1.66×10−27kg.)

v = E/B

R = mv/qB

## The Attempt at a Solution

I found that the selected speed (v) is 2.83 * 10^4 m/s

I got 0.0360 m for the radius of 82Kr

0.0369 m for 84Kr

and 0.0378 m for 86Kr.

My problem is that I don't even understand what it is that they are asking for. What are these adjacent lines that they are talking about? and if there's three isotopes, shouldn't there be three lines?

You haven't included the image so I can't be certain, but usually the ions that are selected will follow circular arcs of radii that depend upon their mass before they impact on a target. Where they impact they produce an image, either a spot or line depending upon details of the equipment. Presumably they are looking for the distance separating such individual lines. If it turns out that the spacing is even, then any two adjacent lines will do. Perhaps the problem text should have read, "...find the distance between the two adjacent lines formed by the three isotopes..."

gneill said:
You haven't included the image so I can't be certain, but usually the ions that are selected will follow circular arcs of radii that depend upon their mass before they impact on a target. Where they impact they produce an image, either a spot or line depending upon details of the equipment. Presumably they are looking for the distance separating such individual lines. If it turns out that the spacing is even, then any two adjacent lines will do. Perhaps the problem text should have read, "...find the distance between the two adjacent lines formed by the three isotopes..."
sorry I forgot about the image.

https://session.masteringphysics.com/problemAsset/1266175/5/22.jpg
gneill said:
You haven't included the image so I can't be certain, but usually the ions that are selected will follow circular arcs of radii that depend upon their mass before they impact on a target. Where they impact they produce an image, either a spot or line depending upon details of the equipment. Presumably they are looking for the distance separating such individual lines. If it turns out that the spacing is even, then any two adjacent lines will do. Perhaps the problem text should have read, "...find the distance between the two adjacent lines formed by the three isotopes..."
Sorry I forgot about the picture.

#### Attachments

• physics.jpg
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Okay, it looks like I was correct; You want to find the distance between adjacent impact locations on the particle detector target.

Wouldn't that be the difference in radii between two adjacent isotopes? For instance, (Radius for 84Kr) - (Radius for 82Kr) = 0.9 mm?

Elvis 123456789 said:
Wouldn't that be the difference in radii between two adjacent isotopes? For instance, (Radius for 84Kr) - (Radius for 82Kr) = 0.9 mm?
Examine the diagram carefully. How far from the selector exit port do the ions land? Is it one radius away?

gneill said:
Examine the diagram carefully. How far from the selector exit port do the ions land? Is it one radius away?
ah I see, they all land one diameter away. so 2*[(Radius of 84Kr) - (Radius of 82Kr)]?

Elvis 123456789 said:
ah I see, they all land one diameter away. so 2*[(Radius of 84Kr) - (Radius of 82Kr)]?
Sure.

gneill said:
Sure.
Ok awesome, thank you kind sir.

## 1. What is the distance between isotopes in a mass spec?

The distance between isotopes in a mass spec refers to the difference in mass-to-charge ratio (m/z) between two isotopes of the same element. This distance is typically measured in atomic mass units (amu).

## 2. How is the distance between isotopes in a mass spec measured?

The distance between isotopes in a mass spec is measured using a mass spectrometer, which separates ions based on their m/z ratios. The ions are then detected and recorded, allowing scientists to determine the distance between different isotopes.

## 3. Why is the distance between isotopes important in mass spectrometry?

The distance between isotopes is important in mass spectrometry because it allows scientists to identify and distinguish between different isotopes of the same element. This information is crucial in determining the chemical composition of a sample and can aid in identifying unknown substances.

## 4. Can the distance between isotopes vary for different elements?

Yes, the distance between isotopes can vary for different elements. This is because each element has a unique atomic mass and thus different isotopes will have different m/z ratios. For example, the distance between isotopes of carbon (C) will be different than the distance between isotopes of nitrogen (N).

## 5. How does the distance between isotopes impact the accuracy of mass spectrometry results?

The distance between isotopes can impact the accuracy of mass spectrometry results by affecting the resolution of the instrument. If the distance between isotopes is too small, it can be difficult to distinguish between them, leading to inaccurate results. Therefore, it is important for mass spectrometers to have high resolution in order to accurately measure the distance between isotopes.

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