In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked $A , B , C , D$ and $E$. The transitions $A, B$ and $C$ respectively represent :
- The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.
- The first member of the Lyman series, third member of Balmer series and second member of Paschen series.
- The series limit of Lyman series, third member of Balmer series and second member of Paschen series.
- The series limit of Lyman series, second member of Balmer series and second member of Paschen series.
The Correct Option is C
Solution and Explanation
The given question involves identifying the transitions in a hydrogen atom that correspond to specific series in the emission spectrum. Let's analyze the question and the options provided to determine the correct answer.
In the hydrogen spectrum, the emitted wavelengths are categorized into several series according to the final energy level of the electron:
- Lyman Series: Transitions to \(n_1 = 1\). This includes transitions such as \(n = 2 \to n = 1\) (first member), \(n = 3 \to n = 1\) (second member), etc.
- Balmer Series: Transitions to \(n_1 = 2\). Examples include \(n = 3 \to n = 2\) (first member), \(n = 4 \to n = 2\) (second member), etc.
- Paschen Series: Transitions to \(n_1 = 3\). This series starts with \(n = 4 \to n = 3\) (first member), \(n = 5 \to n = 3\) (second member), etc.
Given the options, we are to identify the transitions \(A\), \(B\), and \(C\) as follows:
- A - The series limit of the Lyman series: This represents the ionization of a hydrogen atom, i.e., the transition from \(n = \infty\) to \(n = 1\).
- B - Third member of the Balmer series: This corresponds to the transition \(n = 5 \to n = 2\).
- C - Second member of the Paschen series: This describes the transition \(n = 5 \to n = 3\).
Therefore, the correct answer is: "The series limit of the Lyman series, third member of Balmer series, and second member of Paschen series."
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Concepts Used:
Bohr's Model of Hydrogen Atom
Niels Bohr introduced the atomic Hydrogen model in 1913. He described it as a positively charged nucleus, comprised of protons and neutrons, surrounded by a negatively charged electron cloud. In the model, electrons orbit the nucleus in atomic shells. The atom is held together by electrostatic forces between the positive nucleus and negative surroundings.
Read More: Bohr's Model of Hydrogen Atom
Bohr's Theory of Hydrogen Atom and Hydrogen-like Atoms
A hydrogen-like atom consists of a tiny positively-charged nucleus and an electron revolving around the nucleus in a stable circular orbit.
Bohr's Radius:
If 'e,' 'm,' and 'v' be the charge, mass, and velocity of the electron respectively, 'r' be the radius of the orbit, and Z be the atomic number, the equation for the radii of the permitted orbits is given by r = n2 ｘr1, where 'n' is the principal quantum number, and r1 is the least allowed radius for a hydrogen atom, known as Bohr's radius having a value of 0.53 Å.
Limitations of the Bohr Model
The Bohr Model was an important step in the development of atomic theory. However, it has several limitations.
- Bohr’s model of the atom failed to explain the Zeeman Effect (effect of magnetic field on the spectra of atoms).
- It failed to explain the Stark effect (effect of electric field on the spectra of atoms).
- The spectra obtained from larger atoms weren’t explained.
- It violates the Heisenberg Uncertainty Principle.