Question

The electron in the hydrogen atom undergoes the transition from higher orbitals to the orbital of radius $211.6{\text{ pm}}$ . This transition is associated with:
A.Brackett series
B.Lyman Series
C.Paschen Series
D.Balmer Series

Answer 1

Hint: To answer this question, you should recall the concept of spectral lines of a hydrogen atom, Bohr’s theory and the various transition series when an excited electron comes back to the lower energy state. Once the electrons in the gas are excited, they make transitions between the energy levels.

Formula used:
\[{{\text{r}}_{\text{n}}} = 52.9{\text{pm}} \times {{\text{n}}^{\text{2}}}\]
where \[{{\text{r}}_{\text{n}}}\] is the radius of orbit and \[{\text{n}}\] is the shell number.

Complete step by step answer:
According to Bohr's theory, the electrons in an atom after receiving incident energy move from a lower energy level to a higher energy level. This phenomenon occurs by the gain of energy. When an electron moves from a higher energy level to lower energy level by losing energy, the energy is lost in the form of spectral lines.
Hence, spectral series can be defined as a set of wavelengths arranged sequentially with the characteristic feature of every atom. The emitted wavelengths are resolved using a spectroscope. Also, this model states that negatively charged particles called electrons revolve around the positively charged nucleus in a definite circular path called orbits or shells. These shells have a fixed energy state which is different for every shell.
The shells are designated with integers \[\left( {n = 1,{\text{ }}2,{\text{ 3}}.....} \right)\]
This value \[n\]is called the principal quantum number. We are given the radius of the orbit; hence the equation can be written as:
\[{{\text{r}}_{\text{n}}} = 52.9{\text{pm}} \times {{\text{n}}^{\text{2}}}\],
Substituting the given radius and solving:
\[ \Rightarrow 211.6{\text{pm}} = 52.9{\text{pm}} \times {{\text{n}}^{\text{2}}}\]
\[ \Rightarrow {n^2} = 4\]
Solving this for n, we get:
\[n = 2\]
Hence, the transition is from a higher orbit to the second orbit. This corresponds to the Balmer series.

Thus, the correct option is D.

Note:
Limitations of Bohr’s Model of an Atom
-Bohr’s model was not able to explain the Zeeman Effect. It is defined as the splitting of the spectral lines in presence of the magnetic field.
-It was not able to explain the Stark effect which is the splitting of spectral lines in presence of an electric field.
-It violates the Heisenberg Uncertainty Principle.
-It could not explain the spectra obtained from larger atoms.