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

A massa atômica de um elemento obtido de diferentes fontes muda ligeiramente devido à variação na concentração relativa de isótopos de uma fonte para outra. Este é um exemplo de incerteza decorrente de um erro sistemático.
Aqui, a distribuição das massas atômicas é retangular, ao contrário da distribuição gaussiana observada em erros aleatórios. Isso significa que há uma probabilidade aproximadamente igual de encontrar valores entre os valores mais baixos e mais altos.
O desvio padrão ou incerteza padrão calculado a partir do gráfico serve como uma medida de incerteza.
As incertezas individuais de diferentes átomos que compõem uma molécula contribuem para a incerteza líquida na massa molecular.
A propagação da incerteza sistemática na massa molecular de uma molécula heteroatômica é estimada multiplicando o número de átomos idênticos por suas incertezas padrão, seguida pela soma dos quadrados das incertezas padrão totais de todos os elementos presentes na molécula e, finalmente, encontrando a raiz quadrada.

propagação da incerteza a partir do erro sistemático

A massa atômica de um elemento varia devido à proporção relativa de seus isótopos. A proporção relativa de isótopos de oxigênio de uma amostra influencia sua massa atômica média. Por exemplo, se medíssemos a massa atômica do oxigênio de uma amostra, a massa seria uma média ponderada das massas isotópicas do oxigênio nessa amostra. Como uma única amostra provavelmente não refletirá perfeitamente a verdadeira massa atômica do oxigênio para todas as moléculas de oxigênio na Terra, a massa que obtivermos dessa amostra específica dará origem a um erro de amostragem ou a um tipo de erro sistemático. Isso significa que há uma incerteza na massa atômica do oxigênio. Não é um erro aleatório, mas específico do sistema ou um erro sistemático. A probabilidade de encontrar um determinado valor é a mesma dentro da faixa de incerteza. O gráfico de distribuição de valores tem formato retangular. Com um corte nítido na frequência de ocorrência nos valores mínimo e máximo relatados, os valores intermediários têm aproximadamente a mesma frequência de aparecimento. Isso difere da distribuição gaussiana de valores com erros aleatórios, onde a frequência de ocorrência é alta perto do valor central ou médio e diminui à medida que o valor se desvia da média.

O desvio padrão ou incerteza padrão obtido do gráfico de distribuição retangular pode ser usado para medir a incerteza. As incertezas individuais dos átomos constituintes de uma molécula se propagam para a incerteza de sua massa molecular. A propagação dos erros sistemáticos não segue as mesmas regras dos erros aleatórios. Como os erros sistemáticos não é reduzidos por medições repetidas, a sua propagação é muito mais aditiva. Considere o seguinte exemplo: Em uma molécula contendo múltiplos átomos idênticos, a incerteza na massa de um átomo é multiplicada pelo número de átomos semelhantes para obter a contribuição total da incerteza para a massa molecular desses átomos específicos. Se heteroátomos estiverem presentes em uma molécula, a incerteza na massa molecular é a raiz quadrada da soma dos quadrados das incertezas totais de cada tipo de átomo presente.

Propagação da Incerteza a partir do Erro Sistemático

A massa atômica de um elemento obtido de diferentes fontes muda ligeiramente devido à variação na concentração relativa de isótopos de uma fonte para ...

Education

JoVE Core

Analytical Chemistry

Química Analítica

Unit 1

Unidade 1

Chemical Applications of Statistical Analyses

Aplicações Químicas de Análises Estatísticas

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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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