Niels Bohr

The Bohr model of germanium is a simplified representation of the germanium atom proposed by Niels Bohr in 1913. It describes the electrons in germanium atoms as orbiting the nucleus in fixed circular paths, or energy levels, and helps explain the electronic structure of germanium. The model was an important step in the development of quantum mechanics.

Bohr's atomic model depicts the electron shells and orbitals as being two dimensional, staying the exact same distance away from the nucleus the entire time. Today, we know that electron orbits are three dimensional, and at best can only say where the electron in a given orbital is most likely to be at any given time, except for the f orbitals, as no one really knows for sure what those look like yet.

Niels Bohr was a Danish physicist known for his model of the atom, which posited that electrons orbit the atomic nucleus in discrete energy levels. This model, known as the Bohr model, helped explain atomic spectra and laid the foundation for later developments in quantum mechanics. Bohr's work was crucial in shaping our understanding of the structure of atoms and the behavior of electrons within them.

The Bohr model of the atom, which placed electrons at specific energy levels around the nucleus, is known as the planetary model of the atom. In this model, electrons orbit the nucleus in fixed paths or "shells."

I don't know whether there is such a thing as "Schrödinger's atomic theory". That may refer to his "wave function". As far as I know, Schrödinger's wave function is one of the most accurate descriptions of nature so far.

Reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the unit of mass, which allows the two-body problem to be solved as if it were a one-body problem. Note however that the mass determining the gravitational force is not reduced. In the computation one mass can be replaced by the reduced mass, if this is compensated by replacing the other mass by the sum of both masses.

Given two bodies, one with mass m_{1}\!\, and the other with mass m_{2}\!\,, they will orbit the barycenter of the two bodies. The equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass

m_\text{red} = \mu = \cfrac{1}{\cfrac{1}{m_1}+\cfrac{1}{m_2}} = \cfrac{m_1 m_2}{m_1 + m_2},\!\,

where the force on this mass is given by the gravitational force between the two bodies. The reduced mass is always less than or equal to the mass of each body and is half of the harmonic mean of the two masses.

This can be proven easily. Use Newton's second law, the force exerted by body 2 on body 1 is

F_{12} = m_1 a_1. \!\,

The force exerted by body 1 on body 2 is

F_{21} = m_2 a_2. \!\,

According to Newton's third law, for every action there is an equal and opposite reaction:

F_{12} = - F_{21}.\!\,

Therefore,

m_1 a_1 = - m_2 a_2. \!\,

and

a_2=-{m_1 \over m_2} a_1. \!\,

The relative acceleration between the two bodies is given by

a= a_1-a_2 = \left({1+{m_1 \over m_2}}\right) a_1 = {{m_2+m_1}\over{m_1 m_2}} m_1 a_1 = {F_{12} \over m_\text{red}}.

So we conclude that body 1 moves with respect to the position of body 2 as a body of mass equal to the reduced mass.

Alternatively, a Lagrangian description of the two-body problem gives a Lagrangian of

L = {1 \over 2} m_1 \mathbf{\dot{r}}_1^2 + {1 \over 2} m_2 \mathbf{\dot{r}}_2^2 - V(\vert \mathbf{r}_1 - \mathbf{r}_2 \vert ) \!\,

where m_i, \mathbf{r}_i are the mass and position vector of the i th particle, respectively. The potential energy V takes this functional dependence as it is only dependent on the absolute distance between the particles. If we define \mathbf{r} \equiv \mathbf{r}_1 - \mathbf{r}_2 and let the centre of mass coincide with our origin in this reference frame, i.e. m_1 \mathbf{r}_1 + m_2 \mathbf{r}_2 = 0 , then

\mathbf{r}_1 = \frac{m_2 \mathbf{r}}{m_1 + m_2} , \mathbf{r}_2 = \frac{-m_1 \mathbf{r}}{m_1 + m_2}.

Then substituting above gives a new Lagrangian

L = {1 \over 2}m_\text{red} \mathbf{\dot{r}}^2 - V(r),

where m_\text{red} = \frac{m_1 m_2}{m_1 + m_2} , the reduced mass. Thus we have reduced the two-body problem to that of one body.

The reduced mass is frequently denoted by the Greek letter \mu\!\,; note however that the standard gravitational parameter is also denoted by \mu\!\,.

In the case of the gravitational potential energy V(\vert \mathbf{r}_1 - \mathbf{r}_2 \vert ) = - G m_1 m_2 / \vert \mathbf{r}_1 - \mathbf{r}_2 \vert\!\, we find that the position of the first body with respect to the second is governed by the same differential equation as the position of a body with the reduced mass orbiting a body with a mass equal to the sum of the two masses, because

m_1 m_2 = (m_1+m_2) m_\text{red}\!\,

"Reduced mass" may also refer more generally to an algebraic term of the form

x_\text{red} = {1 \over {1 \over x_1} + {1 \over x_2}} = {x_1 x_2 \over x_1 + x_2}\!\,

that simplifies an equation of the form

\ {1\over x_\text{eq}} = \sum_{i=1}^n {1\over x_i} = {1\over x_1} + {1\over x_2} + \cdots+ {1\over x_n}.\!\,

The reduced mass is typically used as a relationship between two system elements in parallel, such as resistors; whether these be in the electrical, thermal, hydraulic, or mechanical domains. This relationship is determined by the physical properties of the elements as well as the continuity equation linking them.

The model used to describe the behavior of very small particles like electrons orbiting an atom is the quantum mechanical model. This model incorporates principles of quantum mechanics to describe the probability of finding an electron at different locations around the nucleus of an atom.

The Bohr model describes the atom as having a small positively charged nucleus at the center, surrounded by negatively charged electrons orbiting in specific energy levels or shells. These energy levels are quantized, meaning the electrons can only occupy certain allowed orbits. The model helped explain the stability of atoms and the emission/absorption of light by electrons moving between energy levels.

Sorry! Adobe can only help you like any graphic design software.

There are a lot software to designer electronic circuit, those allow you to set virtual component in the computer and emulate the circuit and other applications like print the schematic.

because the electric field of the nucleolus is radially symmetrical.

And if you really want to get picky, the electron doesn't move in a circle but occupies a spherical probability continuum with indeterminable position and velocity.

Niels Bohr's hobbies included playing tennis, skiing, and hiking. He was also known to have a passion for music and played the piano.

Niels Bohr's key hypothesis was that electrons orbit the nucleus in specific energy levels or orbits, and they can only transition between these levels by absorbing or emitting specific amounts of energy. This hypothesis explained the discrete pattern of atomic spectra by linking the spectral lines to the energy differences between electron orbits.

Niels Bohr used copper in his experiment on the electromagnetic radiation emitted by metals when heated.

The Bohr model was made around 1913. There isn't an exact date, it's unknown.

D electrons exist in - This statement is not true about Bohr's model of the atom because Bohr proposed that electrons move in quantized orbits around the nucleus, rather than existing as continuous particles.

Bohr's model of the atom compares electrons to planets orbiting around the sun. In the same way that planets have stable orbits around the sun, electrons have stable orbits around the nucleus of an atom.

Ernest Rutherford is known for his discovery of the atomic nucleus and the Rutherford model of the atom. Niels Bohr, on the other hand, proposed the Bohr model of the atom, which introduced the concept of quantized electron orbits. Both scientists made significant contributions to the field of atomic theory.

Niels Bohr was sub-atomic in height. This is how he figured out how atoms work. Wolfgang Pauli was even smaller, which is how he knew about electrons. They teamed up for a film in the twenties, but no one could see them. It was merely postulated that they were there.

The Bohr model describes lead as having a nucleus at the center with 82 protons and usually 125 neutrons. Electrons orbit the nucleus in energy levels or shells. The electron configuration for lead is [Xe] 4f14 5d10 6s2 6p2.

No, Bohr's atomic model does not look like an onion. It represents the atom as a small, positively charged nucleus surrounded by orbiting electrons in fixed energy levels. The model is more complex and based on quantum mechanics principles.

These are examples of natural sources of contaminants such as pollutants, pesticides, and heavy metals that can pose health risks if consumed in high amounts. It is important to be aware of these sources and take measures to minimize exposure.

Niels Bohr's wife was Margrethe Nørlund.

The Bohr model was an attempt to explain the structure of the hydrogen atom, specifically the discrete energy levels of electrons and the transitions between these levels that produce spectral lines. It proposed that electrons orbit the nucleus in fixed circular paths at specific distances, or energy levels.

You draw the 7 protons (atomic number is 7 so it has 7 protons), and 7 neutrons (the atomic weight minus the atomic number(14-7=7) so 7 neutrons). You now draw two circles around the protons and neutrons, these are called electron shells. Since nitrogen has 7 electrons you draw 2 in the first ring (the maximum for the first layer), and 5 in the second layer. For example if you had Calcium (atomic number 20), then the electron shells will hold 2 electrons, 8 electrons, 8 electrons, and then 2 electrons. It gets a bit more difficult after 20.

The wave model of electron placement, described by Schrödinger's equation, considers electrons as standing waves of probability distributions around the nucleus, indicating the likelihood of finding an electron in a specific region. In contrast, Niels Bohr's model proposes discrete electron orbits at fixed energy levels around the nucleus, with electrons moving in specific circular paths. Bohr's model does not account for the wave-like behavior of electrons or their inherent uncertainty in position.