Q.The diameter of the Sun is about $1.4\times10^{9}$ m and the diameter of a hydrogen atom is about $1\times10^{-10}$ m. Estimate the order of magnitude of the ratio of these two sizes.

Order of Magnitude and Physical Scales

An order‑of‑magnitude estimate expresses a quantity as the nearest power of ten, letting one compare vastly different scales and check the plausibility of answers. Physics spans about $40$ orders of magnitude, from sub‑nuclear ($10^{-15}$ m) to cosmic ($10^{26}$ m) distances.

Typical estimates use simple relations:

• Astronomical distances: the Sun is ≈ $1.5\times10^{11}$ m and the Moon ≈ $3.8\times10^{8}$ m from Earth, so their ratio is of order $10^{2}–10^{3}$.
• Molecular mass: the mass of one molecule is (molar mass)/(Avogadro number); for water, $m \approx \dfrac{18\times10^{-3}}{6.0\times10^{23}} \approx 3\times10^{-26}$ kg. …