4. Typical measurements of the mass of a A particle (1230 MeV/c²) are shown in the figure. Although the lifetime of the delta is much too short to measure directly, it can be calculated from the energy- time uncertainty principle. Estimate the lifetime from the full width at half-maximum of the mass measurement distribution shown. ние Each lin hawidh 1000 1100 1200 1500 1400 1500 Man of the dels particle M/

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**Transcription for Educational Website:**

4. **Delta Particle Mass Measurement**

The typical measurements of the mass of a Δ (Delta) particle, approximately 1230 MeV/c², are depicted in the figure. Although the lifetime of the delta particle is too brief to measure directly, it can be inferred using the energy-time uncertainty principle. The task is to estimate the lifetime from the full width at half-maximum (FWHM) of the mass measurement distribution provided.

**Graph Explanation:**

- **X-Axis:** Represents the mass of the delta particle in MeV/c², ranging from 1000 to 1600 MeV/c².
- **Y-Axis:** Indicates the number of data measurements, showing the frequency of each mass measurement value.
- **Curve:** A bell-shaped curve representing the distribution of mass measurements. The peak of this curve is centered around the mean mass value of the delta particle.
- **Each Bin Width:** The graph specifies that each bin in the histogram has a width of 25 MeV/c², allowing for a detailed examination of the distribution.

This visualization aids in understanding the typical mass range of the Δ particle and provides a means to estimate its lifetime using the principles of quantum mechanics.
Transcribed Image Text:**Transcription for Educational Website:** 4. **Delta Particle Mass Measurement** The typical measurements of the mass of a Δ (Delta) particle, approximately 1230 MeV/c², are depicted in the figure. Although the lifetime of the delta particle is too brief to measure directly, it can be inferred using the energy-time uncertainty principle. The task is to estimate the lifetime from the full width at half-maximum (FWHM) of the mass measurement distribution provided. **Graph Explanation:** - **X-Axis:** Represents the mass of the delta particle in MeV/c², ranging from 1000 to 1600 MeV/c². - **Y-Axis:** Indicates the number of data measurements, showing the frequency of each mass measurement value. - **Curve:** A bell-shaped curve representing the distribution of mass measurements. The peak of this curve is centered around the mean mass value of the delta particle. - **Each Bin Width:** The graph specifies that each bin in the histogram has a width of 25 MeV/c², allowing for a detailed examination of the distribution. This visualization aids in understanding the typical mass range of the Δ particle and provides a means to estimate its lifetime using the principles of quantum mechanics.
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