A common technique in the analysis of scientific data is normalization. The purpose of normalizing data is to eliminate irrelevant constants that can obscure the salient features of the data. The goal of this experiment is to test the hypothesis that the flux of light decreases as the square of the distance from the source. In this case, the absolute value of the voltage measured by the photometer is irrelevant; only the relative value conveys useful information.

Suppose that in Part 2.2.2 of the experiment, students obtain a signal value of 181 mV at a distance of 4.2 cm and a value of 80 mV at a distance of 6.1 cm. Normalize the students' data to the value obtained at 4.2 cm (divide the signal value by 181). Then calculate the theoretically expected (normalized) value at 6.1 cm.

1. Normalized experimental value at 6.1 cm:
2. Theoretically expected normalized value at 6.1 cm:

Question

01-01-2024
Engineering

College

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A common technique in the analysis of scientific data is normalization. The purpose of normalizing data is to eliminate irrelevant constants that can obscure the salient features of the data. The goal of this experiment is to test the hypothesis that the flux of light decreases as the square of the distance from the source. In this case, the absolute value of the voltage measured by the photometer is irrelevant; only the relative value conveys useful information.

Suppose that in Part 2.2.2 of the experiment, students obtain a signal value of 181 mV at a distance of 4.2 cm and a value of 80 mV at a distance of 6.1 cm. Normalize the students' data to the value obtained at 4.2 cm (divide the signal value by 181). Then calculate the theoretically expected (normalized) value at 6.1 cm.

1. Normalized experimental value at 6.1 cm:
2. Theoretically expected normalized value at 6.1 cm:

Answer :

Final answer:

The normalized value at 6.1cm is calculated as 80/181 or 0.442. Theoretically, it should be (4.2/6.1)^2 or 0.47 since intensity should decrease with the square of the distance from the source. The difference between these values suggests small errors or other influencing factors.

Explanation:

Given that the signal value at 4.2 cm is 181 mV, we first normalize the data by dividing the signal value at 6.1 cm by 181 mV. Hence, the Normalized experimental value at 6.1 cm is 80/181 = 0.442.

Theoretically, based on the inverse square law, the intensity (flux) should decrease with the square of the distance from the source. Therefore, if we normalize this theoretical value to the measurement at 4.2 cm, the signal at 6.1 cm should be (4.2/6.1)^2 = 0.47.

Observing the results, while there is some difference between our experimental normalized value and the theoretically expected normalized value, the general trend follows the inverse square law. This indicates that the hypothesis may be correct, though factors like measurement error or other variables like the specific photometer used could affect results, specifically as the photometer is irrelevant to the relative values we're interested in.

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Answer :

Final answer:

Explanation:

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