Fundamental particle masses: given that the mass of a neutron is about 1839 times the mass of an electron, what is the approximate ratio of the mass of a proton to the mass of an electron (use the standard rounded textbook value)?

Introduction / Context:
The relative masses of the three basic sub-atomic particles (electron, proton, neutron) are staple facts in physics and chemistry. They underpin atomic structure, isotope behavior, spectroscopic shifts, and many order-of-magnitude estimates in nuclear and particle problems. This question asks you to recall (or quickly estimate) the proton-to-electron mass ratio when you are told the neutron-to-electron ratio for reference.

Given Data / Assumptions:

• Neutron mass ≈ 1839 times electron mass (rounded classroom value).
• We need the proton mass ratio relative to the electron.
• Use widely taught rounded integers suitable for MCQ contexts.

Concept / Approach:
Standard constants provide these approximate ratios: m_p / m_e ≈ 1836 to 1837 and m_n / m_e ≈ 1839. The neutron is slightly heavier than the proton, so the proton ratio must be a little less than the neutron ratio. Textbook MCQs commonly offer 1836 or 1837; when one choice is 1837, it matches the expected rounded value and the inequality m_p < m_n remains consistent.

Step-by-Step Solution:
Identify known rounded ratios: m_p / m_e ≈ 1836–1837; m_n / m_e ≈ 1839.Compare: proton is slightly lighter than neutron, so ratio should be just below 1839.Scan the options and select 1837 as the nearest standard rounded value.Reject values that are implausibly small (159), excessively large (10000), or nonstandard (2537, 918.5).

Verification / Alternative check:
From physical constants, m_p ≈ 1.6726e−27 kg, m_e ≈ 9.109e−31 kg → m_p / m_e ≈ 1836.15. Rounded MCQ keys often use 1836 or 1837; with neutron given as 1839, picking 1837 maintains correct ordering m_e < m_p < m_n.

Why Other Options Are Wrong:
159: Off by an order of magnitude; does not reflect known constant.2537: Arbitrary and far from accepted value.10000: Physically unrealistic for m_p / m_e.918.5: Roughly half the correct magnitude.

Common Pitfalls:
Memorizing only one ratio (e.g., neutron/electron) and assuming the proton has the same factor; forgetting the proton is slightly lighter than the neutron; or mixing up significant figures beyond what MCQs require.

Final Answer:
1837