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

Die Atommasse eines Elements, die aus verschiedenen Quellen gewonnen wird, ändert sich geringfügig aufgrund der Variation der relativen Isotopenkonzentration von einer Quelle zur anderen. Dies ist ein Beispiel für Unsicherheit, die sich aus einem systematischen Fehler ergibt.
Hier ist die Verteilung der Atommassen rechteckig, im Gegensatz zur Gaußschen Verteilung, die bei Zufallsfehlern beobachtet wird. Das bedeutet, dass die Wahrscheinlichkeit, Werte zwischen dem niedrigsten und dem höchsten Wert zu finden, ungefähr gleich groß ist.
Als Maß für die Unsicherheit dient die aus dem Diagramm berechnete Standardabweichung oder Standardunsicherheit.
Die individuellen Unsicherheiten verschiedener Atome, aus denen ein Molekül besteht, tragen zur Nettounsicherheit in der Molekülmasse bei.
Die Ausbreitung der systematischen Unsicherheit in der Molekülmasse eines heteroatomaren Moleküls wird geschätzt, indem die Anzahl der identischen Atome mit ihren Standardunsicherheiten multipliziert wird, gefolgt von der Summierung der Quadrate der gesamten Standardunsicherheiten aller im Molekül vorhandenen Elemente und schließlich die Quadratwurzel gefunden wird.

weitergabe von unsicherheit durch systematischen fehler

Die Atommasse eines Elements variiert aufgrund des relativen Verhältnisses seiner Isotope. Der relative Anteil an SauerSubstanzisotopen einer Probe beeinflusst ihre durchschnittliche Atommasse. Wenn wir beispielsweise die Atommasse von SauerSubstanz aus einer Probe messen würden, wäre die Masse ein gewichteter Durchschnitt der Isotopenmassen von SauerSubstanz in dieser Probe. Da eine einzelne Probe wahrscheinlich nicht die wahre Atommasse des SauerSubstanzs für alle SauerSubstanzmoleküle auf der Erde perfekt widerspiegelt, führt die Masse, die wir aus dieser bestimmten Probe erhalten, zu Stichprobenfehlern oder einer Art systematischem Fehler. Dies bedeutet, dass die Atommasse des SauerSubstanzs mit Unsicherheit behaftet ist. Es handelt sich nicht um einen zufälligen Fehler, sondern um einen systemspezifischen bzw. systematischen Fehler. Die Wahrscheinlichkeit, einen bestimmten Wert zu finden, ist innerhalb des Unsicherheitsbereichs gleich. Das Verteilungsdiagramm der Werte hat eine rechteckige Form. Während die Häufigkeit des Auftretens bei den gemeldeten Mindest- und Höchstwerten stark abnimmt, treten die Werte dazwischen in etwa gleich häufig auf. Dies unterscheidet sich von der Gaußschen Verteilung von Werten mit zufälligen Fehlern, bei der die Häufigkeit des Auftretens in der Nähe des Zentral- oder Mittelwerts hoch ist und abnimmt, wenn der Wert vom Mittelwert nach außen abweicht.

Die aus dem Rechteckverteilungsdiagramm erhaltene Standardabweichung oder Standardunsicherheit kann zur Messung der Unsicherheit verwendet werden. Die einzelnen Unsicherheiten der Atombestandteile eines Moleküls übertragen sich auf die Unsicherheit seiner Molekülmasse. Die Ausbreitung systematischer Fehler folgt nicht denselben Regeln wie die Ausbreitung zufälliger Fehler. Da systematische Fehler durch wiederholte Messungen nicht reduziert werden, ist ihre Ausbreitung viel additiver. Betrachten Sie das folgende Beispiel: In einem Molekül, das mehrere identische Atome enthält, wird die Unsicherheit der Masse eines Atoms mit der Anzahl ähnlicher Atome multipliziert, um den Gesamtbeitrag der Unsicherheit zur Molekülmasse dieser bestimmten Atome zu erhalten. Wenn Heteroatome in einem Molekül vorhanden sind, ist die Unsicherheit der Molekülmasse die Quadratwurzel der Summe der Quadrate der Gesamtunsicherheiten jeder vorhandenen Atomart.

Weitergabe von Unsicherheit durch systematischen Fehler

Die Atommasse eines Elements, die aus verschiedenen Quellen gewonnen wird, ändert sich geringfügig aufgrund der Variation der relativen Isotopenkonzentration von einer Quelle zu ...

Education

Lehre

JoVE Core

Analytical Chemistry

Analytische Chemie

Unit 1

Einheit 1

Chemical Applications of Statistical Analyses

Chemische Anwendungen statistischer Analysen

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

WICHTIGE BEGRIFFE UND KONZEPTE

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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