Each of the two research groups discovers a new elementary particle. The two reported masses are:

m1 = (7.8
±
0.1)
×
10-27 kg

m2 = (7.0
±
0.2)
×
10-27 kg

What is the discrepancy between the two measurements?

Based on the reported masses, would you say they are likely to be the same particle?

Question

Each of the two research groups discovers a new elementary particle. The two reported masses are:

m1 = (7.8
±
0.1) 
×
10-27 kg

m2 = (7.0
±
0.2) 
×
10-27 kg

What is the discrepancy between the two measurements?

Based on the reported masses, would you say they are likely to be the same particle?

BlackTom AI · Accepted Answer

We start by restating the problem in our own words to focus on what is being asked: two independent measurements of a particle’s mass with uncertainties, and we must determine the discrepancy between the measurements and whether they could correspond to the same particle.
Option-by-option analysis:
Option 1: '0.8 x 10^(-27) kg (not the same particle)'
- The absolute difference between the central values is |7.8 - 7.0| × 10^(-27) kg = 0.8 × 10^(-27) kg. This gives the numerical discrepancy directly from the reported masses.
- To assess whether they could be the same particle, we compare the reported uncertainties: m1 = (7.8 ± 0.1) × 10^(-27) kg gives a range of [7.7, 7.9], and m2 = (7.0 ± 0.2) × 10^(-27) kg gives [6.8, 7.2]. Since these ranges do not overlap, the measurements are inconsistent with each other within the stated uncertainties, making it unlikely they refer to the same particle.
Option 2: '0.8 x10^(-27) kg (the same particle)'
- While the calculated discrepancy of 0.8 × 10^(-27) kg is numerically correct, the reason it’s not appropriate here is the lack of overlap between the uncertainty ranges. The statement that they are the same particle conflicts with the non-overlapping intervals shown above, so this option mischaracterizes the consequence of the uncertainties.
Option 3: '7.4 x10^(-27) kg (the same particle)'
- This proposes a different discrepancy value (7.4 × 10^(-27) kg) that would correspond to a halfway or average distance, but there is no basis for selecting 7.4 from the given data. The problem asks for the discrepancy between the two measurements, which is the absolute difference of central values, not an averaged figure.
Option 4: '7.4 x10^(-27) kg (not the same particle)'
- This option combines the incorrect discrepancy value with the incorrect conclusion about sameness. Since the actual discrepancy between centers is 0.8 × 10^(-27) kg, and because the uncertainty ranges do not overlap, the statement about not being the same particle is correct, but the numerical discrepancy is wrong here and thus this choice is inconsistent.
Synthesis and takeaway:
- The correct numerical discrepancy is 0.8 × 10^(-27) kg, derived from the difference of the central values 7.8 and 7.0 in units of 10^(-27) kg.
- The assessment about whether the two measurements refer to the same particle hinges on whether their uncertainty intervals overlap. Here they do not, so the measurements are unlikely to correspond to the same particle, supporting the conclusion 'not the same particle' for the most accurate option.
- Other options either give an incorrect discrepancy value, or draw the wrong conclusion about sameness (or mix both incorrectly), reflecting common pitfalls such as mixing up the difference, averaging values, or ignoring uncertainties.
Overall, the reasoning shows that the discrepancy is 0.8 × 10^(-27) kg, and the lack of overlap in uncertainties argues against the two measurements representing the same particle.

SPHY001 LAB 6 (Pre-Lab) How to Write the Conclusion of a Laboratory Report | LA010

Each of the two research groups discovers a new elementary particle. The two reported masses are: m1 = (7.8 ± 0.1) × 10-27 kg m2 = (7.0 ± 0.2) × 10-27 kg What is the discrepancy between the two measurements? Based on the reported masses, would you say they are likely to be the same particle?

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