Name: atomic mass uncertainty in isotope samples
Uploaded: 2024-04-04T10:51:11.000Z
Duration: 1 min 10 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.2

CHEM.2.B

propagation-of-uncertainty-from-systematic-error

Propagation of Uncertainty from Systematic Error

La masse atomique d’un élément obtenue à partir de différentes sources change légèrement en raison de la variation de la concentration isotopique relative d’une source à l’autre. Il s’agit d’un exemple d’incertitude découlant d’une erreur systématique.
Ici, la distribution des masses atomiques est rectangulaire, contrairement à la distribution gaussienne observée dans les erreurs aléatoires. Cela signifie qu’il y a une probabilité à peu près égale de trouver des valeurs entre les valeurs les plus basses et les plus élevées.
L’écart-type ou l’incertitude-type calculé à partir du graphique sert de mesure de l’incertitude.
Les incertitudes individuelles des différents atomes qui composent une molécule contribuent à l’incertitude nette de la masse moléculaire.
La propagation de l’incertitude systématique de la masse moléculaire d’une molécule hétéroatomique est estimée en multipliant le nombre d’atomes identiques par leurs incertitudes standard, puis en additionnant les carrés des incertitudes standard totales de tous les éléments présents dans la molécule, et enfin, en trouvant la racine carrée.

propagation de l'incertitude à partir d'une erreur systématique

La masse atomique d'un élément varie en raison du rapport relatif de ses isotopes. La proportion relative d’isotopes de l’oxygène d’un échantillon influence sa masse atomique moyenne. Par exemple, si nous devions mesurer la masse atomique de l’oxygène d’un échantillon, la masse serait une moyenne pondérée des masses isotopiques de l’oxygène dans cet échantillon. Puisqu’il est peu probable qu’un seul échantillon reflète parfaitement la véritable masse atomique de l’oxygène pour toutes les molécules d’oxygène sur Terre, la masse que nous obtiendrons à partir de cet échantillon particulier entraînera à une erreur d’échantillonnage ou à un type d’erreur systématique. Cela signifie qu’il est une incertitude sur la masse atomique de l’oxygène. Il ne s'agit pas d'une erreur aléatoire mais spécifique au système ou d'une erreur systématique. La probabilité de trouver une valeur particulière est la même dans la plage d’incertitude. Le diagramme de distribution des valeurs a une forme rectangulaire. Avec une forte diminution de la fréquence d'apparition aux valeurs minimales et maximales signalées, les valeurs intermédiaires ont à peu près la même fréquence d'apparition. Cela diffère de la distribution gaussienne des valeurs avec des erreurs aléatoires, où la fréquence d'apparition est élevée près de la valeur centrale ou moyenne et diminue à mesure que la valeur s'écarte de la moyenne.

L'écart type ou l'incertitude type obtenu à partir du diagramme de distribution rectangulaire peut être utilisé pour mesurer l'incertitude. Les incertitudes individuelles liées aux atomes constitutifs d'une molécule se propagent à l'incertitude de sa masse moléculaire. La propagation des erreurs systématiques ne suit pas les mêmes règles que celle des erreurs aléatoires. Comme les erreurs systématiques ne sont pas réduites par des mesures répétées, leur propagation est beaucoup plus additive. Prenons l'exemple suivant : dans une molécule contenant plusieurs atomes identiques, l'incertitude sur la masse d'un atome est multipliée par le nombre d'atomes similaires pour obtenir la contribution totale de l'incertitude à la masse moléculaire de ces atomes particuliers. Si des hétéroatomes sont présents dans une molécule, l'incertitude sur la masse moléculaire est la racine carrée de la somme des carrés des incertitudes totales de chaque type d'atome présent.

Propagation de l'incertitude à partir d'une erreur systématique

La masse atomique d’un élément obtenue à partir de différentes sources change légèrement en raison de la variation de la concentration isotopique relative d’une source à ...

Education

Enseignement

JoVE Core

Analytical Chemistry

Chimie analytique

Unit 1

Unité 1

Chemical Applications of Statistical Analyses

Applications chimiques des analyses statistiques

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

atomic mass uncertainty in isotope samples

Atomic mass can vary because different samples contain different isotope ratios. For oxygen, the measured atomic mass is a weighted average of the isotopic masses in that sample. A single sample may not match the true atomic mass of oxygen found across all oxygen molecules on Earth. That creates sampling error, which is a type of systematic error.

This kind of uncertainty is not random. It is tied to the system being measured. Within the uncertainty range, the chance of finding a particular value is the same. The values form a rectangular distribution, with a sharp cutoff at the minimum and maximum reported values. The values in between appear at roughly the same frequency.

This pattern is different from a Gaussian distribution, which is typical of random error. In a Gaussian plot, values cluster near the mean and taper off as they move away from it. The rectangular distribution can be used to find the standard deviation, also called the standard uncertainty. That value describes the uncertainty in the atomic mass measurement.

The uncertainty in individual atoms also affects the uncertainty in a molecule’s mass. Systematic errors do not decrease with repeated measurements, so their propagation is more additive. For a molecule with several identical atoms, the uncertainty for one atom is multiplied by the number of those atoms. If a molecule contains different kinds of atoms, the total molecular mass uncertainty is found by taking the square root of the sum of the squares of the total uncertainties from each atom type.

Atomic Mass Uncertainty in Isotope Samples

atomic-mass-uncertainty-in-isotope-samples

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propagation of uncertainty from systematic error

Atomic mass can vary because different samples contain different isotope ratios. For oxygen, the measured atomic mass is a weighted average of the isotopic masses in that sample. A single sample may not match the true atomic mass of oxygen found across all oxygen molecules on Earth. That creates sampling error, which is a type of systematic error. This kind of uncertainty is not random. It is tied to the system being measured. Within the uncertainty range, the chance of finding a particular...

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key terms and concepts

Explore how isotope ratios affect atomic mass, why systematic uncertainty follows a rectangular distribution, and how atomic uncertainties add into molecular mass.

Atomic Mass Uncertainty in Isotope Samples | JoVE K12

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Atomic Mass Uncertainty in Isotope Samples

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