Notes On Gaseous State This page provides you all details about the gaseous state of BSc standard. Concerned problems will be solved at the end of each concept. Continue till the end to find the easiest explanation of every concept you need in this regard . Postulates of Kinetic Theory of Gases: 1. All gas consist of a very large number of minute particles, called molecules. 2. The gas molecules are extremely small in size and are separated by large distance. The actual volume of the gas molecules is thus negligible as compared to the total volume occupied by the gas. 3. The pressure exerted by the gas is due to the bombardment of the molecules on the walls of the vessel. 4. The gas molecules collide with one another and also with the walls of the vessels. These collisions are perfectly elastic and there is no loss of energy during these collisions. 5. The distance between the gas molecules are very large. Thus, there is no effective force of attraction or r
Hydrogen Spectrum: Details in simple explanation
Electrons of hydrogen atoms when absorb energy, get excited to the next higher shells. These excited electrons emit energy (in form of light), when they jump down to the lower energy levels. These energy (emitted light) are observed on a fluorescent screen which appear as group of lines. The number of lines observed on the screen indicates the number of possible transitions made by excited electrons.
By Rajettan - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=41466201
4. Actual obsevation of line spectrum
The hydrogen spectrum
refers to the specific set of wavelengths of electromagnetic radiation emitted
or absorbed by hydrogen atoms. When hydrogen atoms are excited, typically by
heating or passing an electric current through a gas, they emit light of different
wavelengths.
The hydrogen spectrum is
well-known and has been extensively studied because hydrogen is the simplest
and most abundant element in the universe. The spectrum consists of several
series of spectral lines, which are grouped into different regions based on their
wavelengths.
Types Of Series:There are
mainly 5 types of Hydrogen spectrum series
- Lyman series
- Balmer series
- Paschen series
- Brackett series
- Pfund series
Lyman series:
- This series lies in the ultraviolet (UV) region of the
spectrum. It consists of lines resulting from transitions of electrons
from higher energy levels to the n = 1 (ground) energy level.
- The Lyman series of the hydrogen spectrum consists of
spectral lines that are observed in the ultraviolet (UV) region of the
electromagnetic spectrum. These lines are generated when electrons in
excited states transition to the lowest energy level, which is the n = 1
or ground state.
The Ultraviolet Realm:
- The Lyman series finds its home in the ultraviolet (UV)
region of the electromagnetic spectrum. With wavelengths shorter than
visible light, these lines are beyond the capability of human vision.
Instead, specialized instruments and detectors are employed to study and
analyze this intriguing UV spectrum emitted by excited hydrogen atoms.
Electron Transitions:
- The Lyman series arises from transitions of electrons
within hydrogen atoms. When an electron absorbs energy, either through
heating or an electric current, it moves to a higher energy level, known
as an excited state. Subsequently, as the electron returns to the n = 1
energy level, it emits electromagnetic radiation in the form of UV light.
Each line in the Lyman series corresponds to a specific electron
transition from a higher energy level (n > 1) to the ground state (n =
1).
The Lyman Formula:
- The wavelengths of the Lyman series lines can be described
by the Lyman formula, which captures the relationship between the
wavelength (λ), the Rydberg constant (R_H), and the principal quantum
number (n). The formula is given as:
1/λ = R_H * (1 - 1/n^2)
- This equation allows scientists to calculate the
precise wavelengths associated with the Lyman series lines, aiding in the
identification and characterization of these transitions.
Significance and
Applications:
- The Lyman series has immense scientific importance
across various disciplines. Astrophysicists rely on the observation and
analysis of Lyman series lines to study and understand celestial objects.
By analyzing the absorption and emission spectra of hydrogen in stars,
galaxies, and interstellar media, researchers gain insights into their
composition, temperature, and density. The Lyman series also serves as a
critical tool in the study of intergalactic hydrogen clouds and the early
universe, shedding light on cosmic evolution.
- Furthermore, the Lyman series played a pivotal role in
the development of quantum mechanics. Its existence and the observed
discrete energy levels provided evidence for the quantization of energy
and the wave-particle duality of matter. The success in explaining the
Lyman series with the Bohr model of the hydrogen atom eventually led to
the formulation of more sophisticated quantum mechanical theories.
The Lyman series,
residing in the ultraviolet portion of the electromagnetic spectrum, represents
a crucial component of hydrogen's atomic spectrum. It showcases spectral lines
resulting from electron transitions from higher energy levels to the ground
state. Through its study, scientists have gained significant insights into the
behavior and structure of hydrogen, making remarkable contributions to
astrophysics and quantum mechanics. The Lyman series continues to inspire
further exploration and understanding of the fundamental building blocks of the
universe.
Balmer series:
- This series lies in the visible region of the spectrum
and is the most well-known. It consists of lines resulting from
transitions of electrons from higher energy levels to the n = 2 energy
level. The Balmer series includes the famous four visible lines: H-alpha
(656.3 nm, red), H-beta (486.1 nm, blue-green), H-gamma (434.0 nm,
violet), and H-delta (410.2 nm, violet).
- The Balmer series is indeed a set of spectral lines
that are observed in the visible region of the electromagnetic spectrum.
These lines are generated when electrons in excited states transition to
the n = 2 energy level in hydrogen atoms.
- The Balmer series is named after Johann Balmer, a Swiss
mathematician who discovered an empirical formula to describe the
wavelengths of these spectral lines in 1885. The formula, known as the
Balmer formula, is given by:
1/λ = R_H [(1/2²) - (1/n²)]
- where λ is the wavelength of the emitted or absorbed
light, R_H is the Rydberg constant for hydrogen (approximately 1.097 ×
10^7 m⁻¹), and n is the principal quantum number indicating
the energy level of the electron (n = 3, 4, 5, and so on).
The Balmer series
includes several spectral lines, but the most well-known and prominent lines
are:
- H-alpha (656.3
nm): This
line appears in the red part of the spectrum. It corresponds to the
transition from the n = 3 energy level to the n = 2 energy level.
- H-beta (486.1
nm): This
line appears in the blue-green part of the spectrum. It corresponds to the
transition from the n = 4 energy level to the n = 2 energy level.
- H-gamma (434.0
nm): This
line appears in the violet part of the spectrum. It corresponds to the
transition from the n = 5 energy level to the n = 2 energy level.
- H-delta (410.2
nm): This
line also appears in the violet part of the spectrum. It corresponds to
the transition from the n = 6 energy level to the n = 2 energy level.
These four lines of the
Balmer series are particularly famous and are often used in spectroscopy and
astrophysics. They have been instrumental in studying and understanding the
properties of hydrogen and are frequently observed in various astronomical
objects, including stars and nebulae.
Paschen series:
- This series lies in the infrared (IR) region of the
spectrum. It consists of lines resulting from transitions of electrons
from higher energy levels to the n = 3 energy level.
- The Paschen series is a set of spectral lines observed
in the infrared (IR) region of the electromagnetic spectrum. The lines in
this series are generated when electrons transition from higher energy
levels to the n = 3 energy level in hydrogen atoms.
- The Paschen series is named after Friedrich Paschen, a
German physicist who studied atomic spectra in the late 19th and early
20th centuries. The wavelengths of the lines in the Paschen series can be
described using the following formula, known as the Paschen formula:
1/λ = R_H [(1/3²) - (1/n²)]
- where λ is the wavelength of the emitted or absorbed
light, R_H is the Rydberg constant for hydrogen (approximately 1.097 ×
10^7 m⁻¹), and n is the principal quantum number indicating
the energy level of the electron (n = 4, 5, 6, and so on).
- The Paschen series includes several spectral lines, but
since they lie in the infrared region, they are not visible to the human
eye. These lines are significant for studying hydrogen and its presence in
various astronomical objects, especially in the field of astrophysics.
While the exact
wavelengths of the lines vary, here are a few examples of the Paschen series
lines and their approximate wavelengths:
- Paschen-alpha
(1875.1 nm): Transition
from the n = 4 energy level to the n = 3 energy level.
- Paschen-beta
(1281.8 nm): Transition
from the n = 5 energy level to the n = 3 energy level.
- Paschen-gamma
(1093.1 nm): Transition
from the n = 6 energy level to the n = 3 energy level.
These lines are commonly
observed and studied in infrared spectroscopy, as they provide valuable
information about the energy levels and transitions in hydrogen atoms.
Brackett series:
- This series also lies in the IR region of the
spectrum. It consists of lines resulting from transitions of electrons from
higher energy levels to the n = 4 energy level.
- The Paschen series is a set of spectral lines observed
in the infrared (IR) region of the electromagnetic spectrum. The lines in
this series are generated when electrons transition from higher energy
levels to the n = 3 energy level in hydrogen atoms.
- The Paschen series is named after Friedrich Paschen, a
German physicist who studied atomic spectra in the late 19th and early
20th centuries. The wavelengths of the lines in the Paschen series can be
described using the following formula, known as the Paschen formula:
1/λ = R_H [(1/3²) -
(1/n²)]
- where λ is the wavelength of the emitted or absorbed
light, R_H is the Rydberg constant for hydrogen (approximately 1.097 ×
10^7 m⁻¹), and n is the principal quantum number indicating
the energy level of the electron (n = 4, 5, 6, and so on).
- The Paschen series includes several spectral lines, but
since they lie in the infrared region, they are not visible to the human
eye. These lines are significant for studying hydrogen and its presence in
various astronomical objects, especially in the field of astrophysics.
While the exact
wavelengths of the lines vary, here are a few examples of the Paschen series
lines and their approximate wavelengths:
- Paschen-alpha
(1875.1 nm): Transition
from the n = 4 energy level to the n = 3 energy level.
- Paschen-beta
(1281.8 nm): Transition
from the n = 5 energy level to the n = 3 energy level.
- Paschen-gamma
(1093.1 nm): Transition from the n = 6
energy level to the n = 3 energy level.
These lines are commonly
observed and studied in infrared spectroscopy, as they provide valuable
information about the energy levels and transitions in hydrogen atoms.
Pfund series:
- This series lies in the IR region and represents
transitions to the n = 5 energy level.
- The Pfund series is a set of spectral lines that lie in
the infrared (IR) region of the electromagnetic spectrum. These lines
represent transitions of electrons in hydrogen atoms from higher energy
levels to the n = 5 energy level. The Pfund series is named after August
Herman Pfund, an American physicist who studied atomic spectra in the
early 20th century.
- The wavelengths of the lines in the Pfund series
can be described by the following formula, known as the Pfund formula:
1/λ = R_H [(1/5²) - (1/n²)]
- where λ is the wavelength of the emitted or absorbed
light, R_H is the Rydberg constant for hydrogen (approximately 1.097 ×
10^7 m⁻¹), and n is the principal quantum number indicating
the energy level of the electron (n = 6, 7, 8, and so on).
- Since the Pfund series lines lie in the infrared region
of the spectrum, they are not visible to the human eye. However, they are
of significant importance in spectroscopy, astrophysics, and the study of
hydrogen.
Here are a few examples
of the Pfund series lines and their approximate wavelengths:
- Pfund-alpha (7457
nm): Transition
from the n = 6 energy level to the n = 5 energy level.
- Pfund-beta (4657
nm): Transition
from the n = 7 energy level to the n = 5 energy level.
- Pfund-gamma (4101
nm): Transition
from the n = 8 energy level to the n = 5 energy level.
These lines are commonly
observed and studied in infrared spectroscopy and astrophysical research, as
they provide valuable information about the energy levels and transitions in
hydrogen atoms.
The Pfund series, along
with the Lyman, Balmer, Paschen, and Brackett series, completes the set of
major hydrogen spectral series. Each series represents transitions to a
specific energy level, with the Pfund series corresponding to transitions to
the n = 5 energy level.
The study of these
series played a crucial role in the development of quantum mechanics, as they
provided evidence for the existence of discrete energy levels in atoms and the
quantized nature of electrons. The observation and analysis of these spectral lines
have deepened our understanding of the atomic structure and behavior of
hydrogen, which is the simplest and most abundant element in the universe.
The Pfund series is a
series of infrared spectral lines resulting from transitions of electrons in
hydrogen atoms to the n = 5 energy level. Although these lines are not visible
to the human eye, they are essential for the study of hydrogen and are used in
various fields such as spectroscopy, astrophysics, and quantum mechanics.
Each series can have an
infinite number of lines, but as the energy levels get closer together, the
lines become denser and start to merge into a continuum. The Lyman series has
the highest energy transitions and shortest wavelengths, while the Pfund series
has the lowest energy transitions and longest wavelengths.
The hydrogen spectrum
has played a crucial role in the development of quantum mechanics, as it
provided evidence for the existence of discrete energy levels in atoms and the
quantized nature of electrons.
3. Energy level diagram as straight lines
By Rajettan - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=41466201
4. Actual obsevation of line spectrum
By OrangeDog, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=6278485