Question

A certain transition in the H spectrum from an excited state to ground state in one or more steps gives rise to a total of 10 lines. How many of these belong to the visible region of the spectrum?

Answer 1

Hint: To solve this question, it is required to have knowledge about the spectral lines of H atom and the lines which are present in the visible spectrum. When an electron in H atom is given energy, it reaches an excited state. When this excited electron returns to its ground state, it releases the extra energy in the form of photons. The frequency of the photon is dependent upon the difference in energy states of the different levels. The spectral lines occurring in the Balmer series will lie in the visible region.

Complete step-by-step answer:
As we know that, when an excited electron returns to its ground state, emission occurs as a collection of spectral series rather than one single emission. The different series observed and the energy levels they occur between are:
Lyman series occurring between ${\text{n = 2, 3, 4}}...{\text{ to n = 1}}$.
Balmer series occurring between ${\text{n = 3, 4, 5, 6}}..{\text{ to n = 2}}$
Paschen series occurring between ${\text{n = 4, 5, 6}}..{\text{ to n = 3}}$.
Brackett series occurring between ${\text{n = 5, 6}}..{\text{ to n = 4}}$.
P-fund series occurring between ${\text{n = 6, 7}}...{\text{ to n = 5}}$.
Only the emissions occurring in the Balmer series lie in the visible region and n is the shell number.
Now, we already know that the number of spectral lines possible from an excited state to the ground state is given by the formula: $\sum {\text{n}} $ where n is the excited state. Thus, in the question, it is given as $\sum {{\text{n = 10}}} $. From this, we can conclude that ${\text{n = 4}}$ as $\sum 4 = 4 + 3 + 2 + 1 = 10$. This means that the electron is present in the fourth excited state, i.e. ${\text{n = 5}}$ . So, the number of possible emissions in the Balmer region will be from ${\text{n = 5 to n = 2}}$ , from ${\text{n = 4 to n = 2}}$ and from .${\text{n = 3 to n = 2}}$. . So, the number of spectral lines will be 3.

Note: In the formula to calculate the number of spectral lines, the variable used is helped to identify in which excited state the electron will be. The energy level that electron is present in that particular excited state will be different. For example, the electron is in second excited state means that it is in the third shell or if it is in the fifth excited state then it is in the sixth shell.