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Order Of Magnitude

Easyphysics

An astronomer estimates the diameter of a hydrogen atom as approximately 1.06 angstrom while preparing a scale model of matter. What is the order of magnitude of this diameter in metres?

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About This Question

Subject
physics
Chapter
physics and measurement
Topic
order of magnitude
Difficulty
Easy
Year
2025
Tags
order of magnitudeangstromatomic sizescientific notationpowers of ten

Solution

Correct Answer:

As covered in NCERT Class 11, Chapter 2 (Units and Measurements), the order of magnitude is the power of ten nearest to a quantity when written in standard scientific notation, obtained by rounding the leading coefficient. One angstrom equals 10^{-10} m, so 1.06 angstrom equals 1.06 × 10^{-10} m. Since the coefficient 1.06 is less than the rounding threshold of about 3.16, it rounds down to 1, leaving the order of magnitude as 10^{-10}. The option 10^{-9} is wrong because that corresponds to a nanometre, ten times larger than an angstrom. The option 10^{-11} is wrong as it would require a coefficient below one tenth of an angstrom. The option 10^{-8} is wrong since it overestimates the atomic size by a hundredfold. A sanity check confirms that atomic dimensions are universally quoted on the angstrom scale, which is exactly 10^{-10} m, matching the chosen answer.

This easy difficulty physics question is from the chapter physics and measurement, covering the topic of order of magnitude. It appeared in the 2025 exam.

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