The radius of a hydrogen atom is 10 -10 m. Number of hydrogen atoms n

The radius of a hydrogen atom is 10^-10 m. Number of hydrogen atoms necessary to have a length of one nanometre is :

6.023 × 10<sup>23</sup>

100

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UPSC CAPF – 2015

The radius of a hydrogen atom is given as 10⁻¹⁰ m. We want to find how many hydrogen atoms are needed to form a length of one nanometre (1 nm). One nanometre is equal to 10⁻⁹ metres. To arrange atoms side-by-side to achieve a certain length, we consider their effective diameter. The diameter of a hydrogen atom is approximately 2 times its radius, i.e., 2 * 10⁻¹⁰ m. The number of atoms needed is the total length divided by the diameter of one atom: Number of atoms = (10⁻⁹ m) / (2 * 10⁻¹⁰ m) = (10⁻⁹ / 10⁻¹⁰) / 2 = 10 / 2 = 5.

When stacking spherical objects (like atoms) linearly, the effective length occupied by each object is its diameter.

The size of atoms is typically on the order of angstroms (1 Å = 10⁻¹⁰ m). A nanometre (1 nm = 10⁻⁹ m = 10 Å) is a unit of length often used in nanoscience and technology. This problem provides a basic illustration of scale conversion between atomic dimensions and nanometre scale.

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