Question

What is the diameter of a hydrogen atom in $$nm$$ ?
a.$$1$$
b.$$10$$
c.$$0.1$$
d.$$0.01$$

Answer 1

Hint: Hydrogen atom is the first element of the modern periodic table and therefore has the lowest value of atomic number. The atomic diameter of a hydrogen atom can be determined by finding out its radius and multiplying it by two.

Complete answer:
Bohr's model of an atom is useful in explaining the structure of an atom of mono electronic species like the hydrogen atom.
Hydrogen is the first member of the modern periodic table and has an atomic number of one i.e. the number of protons in the nucleus and electrons in the atom is equal to one.
The structure of a hydrogen atom is such that it contains a dense and compact positively charged nucleus with only one proton present inside it. It only contains a single energy shell that is capable of accommodating two electrons. The shell contains a single electron in its spherically symmetrical s-orbital.
The atomic radius of a hydrogen atom can be calculated by determining the distance between the center of the nucleus and the valence shell containing a single electron. The formula used for calculating this radius was given by Bohr and can be written as follows:
$$r_n={\displaystyle \frac{52.9(n^2)}{Z}}pm$$
Where, $$r_n$$ is the radius of the $$n^{th}$$ energy level. $$n$$ stands for the corresponding energy level and $$Z$$ stands for the atomic number of the atom.
Since, hydrogen atom has a single electron and only one energy level, its radius can be calculated as follows:
$$r_1={\displaystyle \frac{52.9(1^2)}{1}}=52.9pm$$
The radius needs to be doubled and converted to nanometers to get the diameter.
$$diameter=52.9\times 2\times 0.001nm=0.1058nm$$

Hence, the correct option is (c) the diameter of the hydrogen atom is $$0.1nm$$ .

Note:
The nucleus of an atom mainly consists of two types of subatomic particles namely protons and neutrons. Hydrogen is the only element in the modern periodic table that consists of a single proton and zero neutrons in its nucleus.