Question

Which of the following is true when Bohr gave his model for hydrogen atom?
A) It was not known that hydrogen lines could be explained as differences of terms like $R/{n^2}$ with $R$ being a constant and $n$ an integer.
B) It was not known that positive charge is concentrated in a nucleus of small size.
C) It was known that radiant energy occurred in energy bundles defined by $hv$ with $h$ being a constant and $v$ a frequency.
D) Bohr knew terms like $R/{n^2}$ and in the process of choosing allowed the orbits to fit them, he got angular momentum $= nh/2\pi$ as deduction.

Answer 1

Bohr’s model of hydrogen atom was introduced by him in 1913. He described the hydrogen atom as a positively charged nucleus which consisted of protons and neutrons, surrounded by a negatively charged electron cloud. He said that the atom was held together by the forces developed between the positive nucleus and negative surroundings, known as electrostatic forces. Also, the electrons were said to orbit the nucleus in atomic shells.

Complete step by step Solution:
To solve this question, we will evaluate the given options one by one. We will use Bohr’s Postulates, or even more ancient theories, wherever necessary, to verify the given statements.
Option A says ‘It was not known that hydrogen lines could be explained as differences of terms like $R/{n^2}$ with $R$ being a constant and $n$ an integer’
This option is False. Terms like $R/{n^2}$ were used by Bohr himself in his study of hydrogen atoms and hydrogen lines could be explained as differences of such terms even at that time.

Option B says ‘It was not known that positive charge is concentrated in a nucleus of small size’.
This option is also False. It was known since the alpha-particle scattering experiment (performed in 1909) that the positive charge is concentrated in a nucleus of small size. This was one of the conclusions made from the experiment.

Option C says ‘It was known that radiant energy occurred in energy bundles defined by $hv$ with $h$ being a constant and $v$ a frequency’
This option is also False. It was not known at that time that radiant energy occurred in energy bundles defined by $hv$ with $h$ being a constant and $v$ a frequency.

Option D says ‘Bohr knew terms like $R/{n^2}$ and in the process of choosing allowed the orbits to fit them, he got angular momentum $= nh/2\pi$ as deduction’.
This option is true. In 1913, when Bohr gave his theory for hydrogen atom, terms like $R/{n^2}$ were widely known and accepted in the study of atoms, with $R$ being a constant and $n$ an integer. Also, he gave a postulate, called Bohr’s Quantization Rule, which defines the circular path of an electron around the nucleus where the angular momentum of the electron was an integral multiple of $h/2\pi$.

Hence, Option (D) is the correct Answer.

Note: Before Bohr, a number of scientists like Rutherford, Thompson, Dalton, etc. gave their theories of the hydrogen atom. However, none of them was completely true and hence were rejected when a new, more accurate theory came into existence. A brief knowledge of all these theories is necessary for answering questions like these.