The radius of a hydrogen atom is 10-10 m. Number of hydrogen atoms necessary to have a length of one nanometre is :
[amp_mcq option1=”6.023 × 1023” option2=”10″ option3=”5″ option4=”100″ correct=”option3″]
This question was previously asked in
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.