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Bohr’s model explained the experimental data for the hydrogen atom and was widely accepted, but it also raised many questions. We know how matter behaves in the macroscopic world—objects that are large enough to be seen by the naked eye follow the rules of classical physics. When waves interact with each other, they show interference patterns that are not displayed by macroscopic particles such as the billiard ball. As technological improvements allowed scientists to probe the microscopic world in greater detail, it became increasingly clear by the 1920s that very small pieces of matter follow a different set of rules from those we observe for large objects. One of the first people to pay attention to the special behavior of the microscopic world was Louis de Broglie.
Classical angular momentum L for a circular motion is equal to the product of the radius of the circle and the momentum of the moving particle p.
Shortly after de Broglie proposed the wave nature of matter, two scientists at Bell Laboratories, C.
Solution We can use de Broglie’s equation to solve this problem, but we first must do a unit conversion of Planck’s constant. This is a small value, but it is significantly larger than the size of an electron in the classical (particle) view. Check Your Learning Calculate the wavelength of a softball with a mass of 100 g traveling at a velocity of 35 m s–1, assuming that it can be modeled as a single particle.
We never think of a thrown softball having a wavelength, since this wavelength is so small it is impossible for our senses or any known instrument to detect (strictly speaking, the wavelength of a real baseball would correspond to the wavelengths of its constituent atoms and molecules, which, while much larger than this value, would still be microscopically tiny). Werner Heisenberg considered the limits of how accurately we can measure properties of an electron or other microscopic particles. This equation allows us to calculate the limit to how precisely we can know both the simultaneous position of an object and its momentum.
The value of h is not large, so the uncertainty in the position or momentum of a macroscopic object like a baseball is too insignificant to observe.
It should be noted that Heisenberg’s uncertainty principle is not just limited to uncertainties in position and momentum, but it also links other dynamical variables. As will be discussed later, even the vector components of angular momentum cannot all be specified exactly simultaneously.
Read this article that describes a recent macroscopic demonstration of the uncertainty principle applied to microscopic objects. Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, as Bohr had argued, Erwin Schrodinger extended de Broglie’s work by incorporating the de Broglie relation into a wave equation, deriving what is today known as the Schrodinger equation. Schrodinger’s work, as well as that of Heisenberg and many other scientists following in their footsteps, is generally referred to as quantum mechanics. The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them.
This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. The principal quantum number is one of three quantum numbers used to characterize an orbital. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. If an electron has an angular momentum (l ? 0), then this vector can point in different directions. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. The other is called the ? state, with the z component of the spin being negative and ms?=?12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron on [link]) and a higher energy for the magnetic moment being opposite to the applied field. The properties and meaning of the quantum numbers of electrons in atoms are briefly summarized in [link].
Working with Shells and Subshells Indicate the number of subshells, the number of orbitals in each subshell, and the values of l and ml for the orbitals in the n = 4 shell of an atom.
Maximum Number of Electrons Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 5, and (c) n as a variable.
Solution (a) When n = 2, there are four orbitals (a single 2s orbital, and three orbitals labeled 2p). Check Your Learning If a shell contains a maximum of 32 electrons, what is the principal quantum number, n? The ml degeneracy is the number of orbitals within an l subshell, and so is 2l + 1 (there is one s orbital, three p orbitals, five d orbitals, seven f orbitals, and so forth). No two electrons in the same atom can have the same set of values for all the four quantum numbers. Both models have a central positively charged nucleus with electrons moving about the nucleus in accordance with the Coulomb electrostatic potential.
Describe the properties of an electron associated with each of the following four quantum numbers: n, l, ml, and ms. How many electrons could be held in the second shell of an atom if the spin quantum number ms could have three values instead of just two?
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Of course, officially, I’m the transcriptionist for a lab of over 11,000 employees with offices around the world.


Less officially, I’m a writer in Chicago who enjoys reading, improving at Photoshop, and the occasional pop science book. Finally, you can meet zombie Albert Einstein, zombie Carl Sagan, or zombie Nikola Tesla … who do you choose and why?
OverviewFergusson College, Pune was established on 2nd January 1885 by Deccan Education Society (DES).  It is accredited by NAAC in 2004 with A’ Grade. Fergusson College Pune DetailsEligibility Criteria In order to be eligible to the Undergraduate degree courses a candidate should have passed 10+2 from any recognised board. Why did electrons orbit at only fixed distances defined by a single quantum number n = 1, 2, 3, and so on, but never in between?
A billiard ball moving on a table will behave like a particle: It will continue in a straight line unless it collides with another ball or the table cushion, or is acted on by some other force (such as friction). For example, interacting waves on the surface of water can produce interference patters similar to those shown on [link]. The unquestionable separation of waves and particles was no longer the case for the microscopic world. He asked the question: If electromagnetic radiation can have particle-like character, can electrons and other submicroscopic particles exhibit wavelike character? Quantum – Double Slit Experiment cartoon for an easy-to-understand description of wave–particle duality and the associated experiments.
He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. However, the mass of a microscopic object such as an electron is small enough that the uncertainty can be large and significant. For example, when an atom absorbs a photon and makes a transition from one energy state to another, the uncertainty in the energy and the uncertainty in the time required for the transition are similarly related, as ?E ?t ? ?2. The uncertainty principle can be shown to be a consequence of wave–particle duality, which lies at the heart of what distinguishes modern quantum theory from classical mechanics.
When Schrodinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra, and he did so without having to invoke Bohr’s assumptions of stationary states and quantized orbits, angular momenta, and energies; quantization in Schrodinger’s theory was a natural consequence of the underlying mathematics of the wave equation. This story explains the concepts of superposition and entanglement as related to a cat in a box with poison. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside.
It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principle quantum number, n.
It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines.
One is termed the ? state, with the z component of the spin being in the positive direction of the z axis. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. Note you are only looking at the orbitals with the specified n value, not those at lower energies. The Bohr model assumes that the electrons move in circular orbits that have quantized energies, angular momentum, and radii that are specified by a single quantum number, n = 1, 2, 3, …, but this quantization is an ad hoc assumption made by Bohr to incorporate quantization into an essentially classical mechanics description of the atom. It has an  conditioned custom built auditorium, library, laboratories, classrooms, and cafeteria with separate hostel facilities for girls & boys. This university was organized in 2002 under the Islamic International Medical College Trust.
It made me think about how few things I understand at a deep level, so I vowed to dedicate my life to Photoshopping puppies tied to missiles. In retrospect, I think the scientific theme gave me the structure to keep the site going for two years and develop a textbook. I usually mash-up a mix of altered photos, scans of old books, and my own graphs, overlaid with aged textures. I repeatedly get requests from teachers, from the elementary school to college level, for reproductions of my images. Is this an effective means of science communication or does it stop with just being a joke? My science-book tastes probably skew a little lighter than most scientists, but I love reading Oliver Sacks or Dava Sobel, and I just finished Rebecca Skloot’s Henrietta Lacks book. In order to be eligible to the Certificate courses a candidate should have passed 10+2 from any recognised board. Why did the model work so well describing hydrogen and one-electron ions, but could not correctly predict the emission spectrum for helium or any larger atoms? The ball has a well-defined position and velocity (or a well-defined momentum, p = mv, defined by mass m and velocity v) at any given moment. This is a case of wave behavior on the macroscopic scale, and it is clear that particles and waves are very different phenomena in the macroscopic realm. In his 1925 doctoral dissertation, de Broglie extended the wave–particle duality of light that Einstein used to resolve the photoelectric-effect paradox to material particles.
The more accurately we measure the momentum of a particle, the less accurately we can determine its position at that time, and vice versa. Recall that the equations of motion obtained from classical mechanics are trajectories where, at any given instant in time, both the position and the momentum of a particle can be determined exactly. Like de Broglie, Schrodinger initially viewed the electron in hydrogen as being a physical wave instead of a particle, but where de Broglie thought of the electron in terms of circular stationary waves, Schrodinger properly thought in terms of three-dimensional stationary waves, or wavefunctions, represented by the Greek letter psi, ?. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrodinger equation. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. These shapes represent the three-dimensional regions within which the electron is likely to be found. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting.
An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The general region for value of energy of the orbital and the average distance of an electron from the nucleus are related to n. Bohr also assumed that electrons orbiting the nucleus normally do not emit or absorb electromagnetic radiation, but do so when the electron switches to a different orbit. I really like working with look of stuff from the 50s, 60s, and 70s, and acquiring new typefaces from the era. I had to structure it as if I were actually teach science, so I think it’s pedagogically sound (except, of course, for all the facts). Of course, this weighty subject is addressed in the book by showing a scientist who isn’t wearing any pants. The emphasis of the founders on ‘knowledge’ is aptly reflected in the college emblem, which bears the inscription Knowledge is Power. It is affiliated to Pune University. In order to be eligible to the Postgraduate courses a candidate should be a graduate from any recognised University.
To answer these questions, scientists needed to completely revise the way they thought about matter.
Where Bohr had postulated the electron as being a particle orbiting the nucleus in quantized orbits, de Broglie argued that Bohr’s assumption of quantization can be explained if the electron is considered not as a particle, but rather as a circular standing wave such that only an integer number of wavelengths could fit exactly within the orbit ([link]). This is summed up in what we now call the Heisenberg uncertainty principle: It is fundamentally impossible to determine simultaneously and exactly both the momentum and the position of a particle.
Heisenberg’s uncertainty principle implies that such a view is untenable in the microscopic domain and that there are fundamental limitations governing the motion of quantum particles. A few years later, Max Born proposed an interpretation of the wavefunction ? that is still accepted today: Electrons are still particles, and so the waves represented by ? are not physical waves but, instead, are complex probability amplitudes.


A transition to a lower energy level involves a release of energy, and the energy change is negative.
In addition, the principle quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located.
The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. Finally, there are more than one possible orbitals for l ? 1, each corresponding to a specific value of ml.
These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number.
The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. The quantum mechanical model of atoms describes the three-dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ?.
In the quantum mechanical model, the electrons do not move in precise orbits (such orbits violate the Heisenberg uncertainty principle) and, instead, a probabilistic interpretation of the electron’s position at any given instant is used, with a mathematical function ? called a wavefunction that can be used to determine the electron’s spatial probability distribution. The rigors of print quality, from resolution to color, made it a much more complex task than the site, but hopefully more rewarding. It offers various degree courses at undergraduate level and postgraduate level, vocational courses at undergraduate level, special courses at postgraduate level of MCA, M.Sc. Germer, demonstrated experimentally that electrons can exhibit wavelike behavior by showing an interference pattern for electrons travelling through a regular atomic pattern in a crystal.
This does not mean that microscopic particles do not move in trajectories, it is just that measurements of trajectories are limited in their precision. In the case of a hydrogen atom or a one-electron ion (such as He+, Li+, and so on), energies of all the orbitals with the same n are the same. In addition, it cannot be derived from solving the Schrodinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values.
Admission Procedure The application forms for the desired course will be issued in the college itself and the candidate can obtained it   by paying DD of the specified amount and submitting all the documents required by the college. The regularly spaced atomic layers served as slits, as used in other interference experiments. In the realm of quantum mechanics, measurements introduce changes into the system that is being observed.
This is called a degeneracy, and the energy levels for the same principle quantum number, n, are called degenerate energy levels. Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. For l = 2 (d-type orbitals), ml can have values of –2, –1, 0, +1, +2, so we have five 4d orbitals. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in space. The Bohr model gives the same expression for the energy as the quantum mechanical expression and, hence, both properly account for hydrogen’s discrete spectrum (an example of getting the right answers for the wrong reasons, something that many chemistry students can sympathize with), but gives the wrong expression for the angular momentum (Bohr orbits necessarily all have non-zero angular momentum, but some quantum orbitals [s orbitals] can have zero angular momentum).
Since the spacing between the layers serving as slits needs to be similar in size to the wavelength of the tested wave for an interference pattern to form, Davisson and Germer used a crystalline nickel target for their “slits,” since the spacing of the atoms within the lattice was approximately the same as the de Broglie wavelengths of the electrons that they used. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital.
However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies, as shown on [link].
When l = 3 (f-type orbitals), ml can have values of –3, –2, –1, 0, +1, +2, +3, and we can have seven 4f orbitals.
Therefore, atomic orbitals describe the areas in an atom where electrons are most likely to be found.
Orbitals with the same principle quantum number and the same l value belong to the same subshell.
Facilities and InfrastructureThe Fergusson College has its campus spread over 65 acres of land with beautiful view.
The electrons that belong to a specific shell are most likely to be found within the corresponding circular area.
Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. The magnetic quantum number, ml, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level ([link]).
Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The college consists of a central garden surrounded by the period old Main Building and the N. The wave–particle duality of matter can be seen in [link] by observing what happens if electron collisions are recorded over a long period of time. The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. Initially, when only a few electrons have been recorded, they show clear particle-like behavior, having arrived in small localized packets that appear to be random. Wadia Amphitheatre, consists of semi-gothic designed and the imposing height with seating capacity of 1000 and B.
As more and more electrons arrived and were recorded, a clear interference pattern that is the hallmark of wavelike behavior emerged.
And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in [link].
Thus, it appears that while electrons are small localized particles, their motion does not follow the equations of motion implied by classical mechanics, but instead it is governed by some type of a wave equation that governs a probability distribution even for a single electron’s motion. Thus the wave–particle duality first observed with photons is actually a fundamental behavior intrinsic to all quantum particles. It consists of two floors; its first floor is used as spacious Reading Hall for students with capacity of 400. The Main Library on ground floor consists of more than 300000 books and many research journals. Separate buildings for various departments are provided in the campus sprawling from north to south. Large playgrounds, tennis courts, Botanical Garden and spacious hostel buildings are special characteristics of the college. Fergusson College has 6 hostel blocks, 4 blocks for boys and 2 blocks for girls with total intake of 587 students. The college has 100-year-old Botanical Garden, extending over more than 2 acres, contains a wide variety of plants of botanical significance, large number of rare and endangered species and plants having medicinal applications.  It is one of the richest gardens in this part of the country The Botany, Geology, Physics and Zoology departments have their own museums for which special space has been provided by the college. These are storehouses of rare exhibits, which are very great assets for understanding the developments in that subject. College provides medical facilities to provide first aid to the students and faculty, parking facility and recreation centre for extra-curricular activities of students College is provided with sports and gymkhana facilities for various indoor and outdoor games activities.
It consists of table tennis hall, 6 tennis court, 2 badminton halls, 2 basketball court, gymnasium, judo hall etc.
Students participates in various music and dance forms ranging from Vocal singing (Indian Classical, Western Classical, Indian Semi classical, Folk, Light music, etc), Instrumental to Various dance forms (Bharat Natuam, Kathak, Western Classical  and other western dance forms) and various competitions are held to showcase the talent of students to the world. Students also participate in many local, state and national level debate and Quiz competitions. College celebrates departmental festival organized by Economics department and Psychology department such as Wallstreet and Psy-Fy respectively. National service Scheme (NSS) help the students understand community, their relation with community, Social problems.
Various camps and events and activities are conducted by NSS unit and encourage the students participate in it.
Recently, DE Shaw India Software Private Ltd, a global investment and technology development firm, visited Fergusson College and recruited many of its students through personal Interview and GD. Many students of Fergusson College are working as entrepreneur and many of them are studying abroad for higher studies.Ex-Fergussonian Association (EFA) – is the Alumni Association, the organization for former students, faculty and staff - collectively termed "alumni".
The Alumni Association provides a forum for alumni to maintain and develop their links with the College.




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