Which is the smaller atom, Hydrogen or Helium? Question from HSC paper leaves students, teachers, confused

Question B (i) of the Science and Technology (Part 1) paper said, ‘Write the name of the atom having the smallest size.’

Patil’s letter states that going by atomic radius, Helium (31 pm) is smaller than Hydrogen (53 pm) but if one were to consider the van der Waals radius, Hydrogen would be smaller.

In a notification issued on Thursday night, Maharashtra State Board of Secondary and Higher Secondary Education stated that marks will be given to both answers.

Shrimayi Samgir, a 10th standard student of a school in Narayan Peth appearing for her board examinations this year said, “The science paper is usually hard for me but this question was discussed at length after the paper. I answered Helium but some others said that it was Hydrogen instead.”

The official statement said, “The board has been informed that there is confusion among students and parents over this particular question from SSC Science 1 paper held on March 18. Even as correct answer as per the textbook is Helium, in some reference books given answer for the same question in Hydrogen. Considering the situation, it is decided that marks should be given for both answers.”

This confusion is because the physical size of an atom is not often defined or used to describe atoms, especially at the school level. What is used instead is ‘atomic mass’ which refers to the sum of protons and neutrons in the nucleus of an atom and is the basis for the periodic table. This is also one of the reasons for the confusion that the element with the smallest atomic mass (Hydrogen) would also be the smallest in size.

Added to that is the difference between atomic radius and Van der Waals radius raising the question of which scientific measurement exactly is referred to as ‘size’.

Arnab Mukherjee, a researcher at the Chemistry department of IISER said, “When we talk about the size of an atom, we generally refer to the atomic radius, not Van der Waals radius. In this case, that of Helium is less than that of Hydrogen.”

Still acknowledging the opposite argument, he said, “In ordinary circumstances though Hydrogen atoms will form a bond and could together be smaller than Helium whose atoms do not bond.”

Meanwhile, the chief moderator of the Science paper has been intimated about the same, said the Chairperson of Maharashtra State Board of Secondary and Higher Secondary Education, Sharad Gosavi. “Further decisions regarding awarding of marks will be taken by the Board as per the instructions received from the Moderator,” he added.

Breaking the problem down

As the mass of atoms in the periodic table increases from left to right and from top to bottom, it would seem obvious that Hydrogen, appearing in the top left corner, would be the smallest, being the one with the lowest mass.

However the second appearing atom, Helium, is significantly more dense, precisely because its mass is higher while both atoms have only a single shell of electrons. Looking purely at the size of the atom itself, scientifically referred to as the ‘atomic radius’, Helium is thus smaller than Hydrogen.

The answer to the exam question however is not that straightforward. The amount of space an atom occupies is determined by something called the ‘van der Waals radius’. Put simply, this radius determines the minimum distance between two atoms. The bigger the mass of an atom, the larger this radius.

Therefore more Hydrogen atoms can fit in a certain area than Helium atoms, even though Helium is technically smaller. Next to that Hydrogen bonds together in pairs making it even more compact than Helium.