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# Ratio of the Bohr radius of protium, deuterium, and tritium atom is:(A) $1:2:3$(B) $1:1:1$(C) $3:2:1$(D) $2:3:4$

Last updated date: 11th Aug 2024
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Hint: Bohr radius is defined as the distance between the electron and the nucleus of a hydrogen atom in the ground state. It is a physical constant and is denoted by ${a_o }$ or ${r_{bohr}}$ . It is known as Bohr radius due to his prime role in building the Bohr model. Neil Bohr modified the atomic structure model of Rutherford.

Complete step-by-step solution:We know that protium, deuterium and tritium are the isotopes of hydrogen.
Isotopes are the ones which have the same atomic number but different mass number. Thus, the number of neutrons is also different. Mass number is equal to the sum of protons (atomic number) and neutrons.
So, in Protium:
Atomic number $= 1$
Mass number $= 1$
In deuterium:
Atomic number $= 1$
Mass number $= 2$
In Tritium:
Atomic number $= 1$
Mass number $= 3$
We know that the atomic radius changes if there is a change in the atomic number of the atom. It means that the Bohr radius depends upon the atomic number not on the mass number. Therefore, all the three isotopes of hydrogen will have the same Bohr radius as their atomic number is constant.

Additional information: Neil Bohr modified the atomic structure model by explaining that electrons move fixed orbitals or shells and not anywhere in between. He also explained that each shell has a fixed energy level. He modified it because Rutherford basically focused only upon the nucleus of an atom and not upon the electrons and their energy levels.

So, the correct answer is Option B. i.e. $1:1:1$.

Note: The main difference between protium, deuterium and tritium are that protium does not contain neutrons in its nucleus whereas deuterium contains one neutron in its nucleus whereas tritium contains two neutrons. Therefore, we calculate the number of neutrons by subtracting the atomic number from the mass number of the atom.