Bohrs Model of the Atom, Chemistry tutorial

Introduction

In the early 20th century, testings via Ernest Rutherford founded that atoms consisted of a spread cloud of negatively charged electrons surrounding a small, dense, positively charged nucleus. Given this experimental data, Rutherford considered a planetary-model atom, the Rutherford model of 1911: 'electrons orbiting round a solar nucleus' - though, said planetary-model atom has a technical difficulty. The rules of classical mechanics (that is the Larmor formula), predict that the electron will liberate electromagnetic radiation while orbiting a nucleus. Since the electron would lose energy, it would steadily spiral inwards, collapsing into the nucleus. This atom model is disastrous, since it expects that all atoms are unbalanced. As well, as the electron spirals inward, the emission would gradually amplify in frequency as the orbit gets smaller and faster. This would create a continuous smear, in frequency, of electromagnetic radiation. Though, late 19th century experiments through electric discharges have exposed that atoms will only emit light (that is, electromagnetic radiation) at indeed discrete frequencies.

To conquer this complexity, Niels Bohr intended in the year 1913, what is now termed the Bohr model of the atom.

Composition of the Atom

Atoms have a specific structure. This structure finds out the chemical and physical properties of matter. This atomic structure was not entirely implicit until the finding of the neutron in the year 1932. The history of the finding of atomic structure is one of the most concerning and thoughtful stories in science. In the year 1910 Rutherford was the 1st to suggest what is admitted nowadays as the basic structure of the atom. Today, the Rutherford model is termed the "planetary" model of the atom. In the planetary model of the atom, there survives a nucleus at the centre made up of positively charged particles termed 'protons' and electrically neutral particles termed 'neutrons'. Such particles that surround or 'orbit' the nucleus are the electrons. In components, the number of electrons equivalents the no of protons.

2215_Composition of the Atom.jpg

Fig: Composition of the Atom

The Figure above significantly exaggerates the size of the nucleus relative to that of the atom. The nucleus is about 100,000 times lesser than the atom. Nonetheless, the nucleus encloses basically all of the mass of the atom. In order to talk about the mass of an atom, we have to describe a new unit of mass suitable to that of an atom. This new unit of mass is termed the atomic mass unit or amu. The adaptation between the amu and gram is: 

1 amu = 1.67 x10-24 g. The mass, in amu, of the 3 particles is following in the table below:

317_Properties of the Sub-Atomic Particles.jpg

Table: Properties of the Sub-Atomic Particles

As we know that the mass of an electron is about 2000 times smaller than that of the proton and neutron. As well note that the mass of the proton and neutron is seal to 1 amu. This is a helpful fact to remember. If the no of electrons doesn't equivalent the number of protons in the nucleus then the atom is an ion:

  • Cation: number of electrons < number of protons
  • Anion: number of electrons > number of protons

Atomic Excitation and De-Excitation

Atoms can create transitions between the orbits permitted via quantum mechanics through absorbing or releasing exactly the energy dissimilarity between the orbits. Figure demonstrates an atomic excitation reasoned via absorption of a photon and an atomic de-excitation caused by emission of a photon.    

1370_Excitation by  Absorption  of  Light.jpg

Fig: Excitation by Absorption of Light and De-Excitation by Emission of Light

In each case, the wavelength of the produced or absorbed light is equivalent these that the photon carries the energy dissimilarity between the 2 orbits. This energy might be computed via separating the product of the Planck steady and the speed of light hc via the wavelength of the light. Therefore, an atom can absorb or emit only indeed discrete wavelengths (or equivalent frequencies or energies). 

Atomic spectra

After an atom absorbs a quantum of energy, it will be transited to an excited state relative to its normal (ground) state. Whenever an excited atom goes back to the ground state, it releases light. For instance, when glass is warmth in a flame; the yellow light examined that is as a consequence of the excited sodium atoms in the glass being arrival to their ground state.

Likewise, the recognizable red light of neon signs is due to neon atoms which have been excited through an electrical discharge. Whenever light from excited atoms is analyzed during a spectroscope, images of the slit emerge along the scale of the instrument as a sequence of colored lines.

The various colors communicate to light of definite wavelengths, and the series of lines is termed a line spectrum. The line spectrum of each component is the trait of that element and its spectrum might be utilized to recognize it.  The easiest spectrum is that of hydrogen, the simplest element (Figure).

365_Balmer Series  of  Hydrogen Atom.jpg

Fig: Balmer Series of Hydrogen Atom; Spectral Lines in the Visible

The part of the hydrogen spectrum that appears as visible light is following in Figures. It should be mentioned that the lines at shorter wavelengths have increasingly lower intensities. The wavelengths of successive lines are closer and closer together until they finally become a continuum, a district of continuous faint light. In the year 1885, J.J. Balmer proposed that the lines in the visible spectrum of hydrogen could be symbolized through the equation

2273_visible spectrum of hydrogen.jpg

Where is v‾ the wave number (inverse of wavelength), n1 has the value 2, n2 is an integer having the values 3, 4, 5,.... ∞. The value of the constant R is ~ 109,677.581 cm-1. It is recognized as the Rydberg constant.

The Bohr Theory 

Even though the Balmer equation effectively symbolized the hydrogen spectrum, there was no theoretical justification for it.  In the year 1914, Niels Bohr proposed a theory of the hydrogen atom which clarified the origin of its spectrum. This theory as well led to a completely new idea of atomic structure. The Bohr model of the hydrogen atom was depending on 4 postulates.

1st Postulate: The hydrogen atom consists of a nucleus enclosing a proton (and therefore having a charge of +e), and an electron (through a charge of -e) moving about the nucleus in a circular orbit of radius r (Figure). 

1411_The  Force of  Attraction  keeps  bending.jpg

Fig: The  Force of  Attraction  keeps  bending  the  Path  of the Electron  toward the  Nucleus  and away from the  Straight-line Motion

As we know the net consequence is a circular path.

According to Coulomb's law, the force of attraction between the nucleus and the electron is

1891_force of attraction.jpg

Where1883_hydrogen atom.jpgo is the permittivity of the vacuum; Z = 1 for the hydrogen atom) 

This force balances the centrifugal force on the electron, mv2/r, here m is the mass of the electron and v its velocity:

812_mass of the electron.jpg

The kinetic energy of the electron might be computed from this equation also:

Kinetic energy = ½(mv2) =1/8(e2/ π

Note: 

me =   Mass of an electron (9.109 x10-31 kg)

e    =   Quantity of electrical charge (1.602 x10-19 C)

h   =    Planck's constant (6.626 x10-34 Js)

 o =    Vacuum permittivity (8.854 x10-12 C2 N-1 m-2)

c   =   Speed of light (3.0 x108 m s-1)

R =  Rydberg's constant (1.097 x107 m-1)

1 eV = 1.602 x10-19

2nd Postulate: Not all circular orbits are allowed for the electron. Only the orbits that have angular momentum of the electron, m r, and equivalent to integral multiples of h/2π are permitted:

83_integral multiples.jpg

n = 1, 2, 3, 4, 5,...

Equating the 2 expressions for 2 yields and expression for r, the radius of an allowed orbit:

R= n2h2εο/ πme2

The value n = 1 defines the first (smallest) orbit. Larger orbits have higher values for n.

3rd Postulate: As a consequence of the restrictions on the angular momentum of an orbit, the energy of an electron in a following orbit is fixed. As long as the electron stays in that orbit, it neither absorbs nor radiates energy (therefore the orbit is termed a stationary state). The whole energy, E, of an electron is the addition of its potential energy, (negative since the electric force between the electron and the nucleus is attractive and its kinetic energy), (from postulate 1).

Therefore

                  E = -1/8(e2/π εοr)

As a result, the total energy is equal to half the potential energy.  Substituting the expression for r from the above yields

                  E =   - me4/8εο2n2h2

All of the quantities on the right-hand side of this equation are known constants except for the arbitrary integer n. Hence, the possible energies of the electron are determined by the values of n. It should be noted that the negative sign in the energy expression means that the larger the value of n, the higher will be the energy of the electron.

4th Postulate: To transform from one orbit to another, the electron must absorb or release a quantity of energy accurately equivalent to the dissimilarity in energy between the 2 orbits. Whenever light energy is included, the photon has a frequency following via 

h = E2 - E1

Replacement of the analogous energy expression yields. The last equation is the same to the Balmer equation. The constant R might be estimated through using the numerical values of, m, e, c, and h, and the consequence concurs closely through the experimentally found out value for the Rydberg constant.

It follows from the Bohr Theory, since n1 can have values 1, 2, 3, 4, 5, etc., that numerous other series of line should survive in the hydrogen spectrum nearby the Balmer series. Subsequent to the theory, other series have been determined in the ultraviolet, infrared, and far infrared regions of the spectrum. All of such series have lines with wavelengths which are given by the Balmer equation when appropriate values of n1 and n2 are utilized.

Each spectral line represents energy dissimilarity between 2 possible states of the atom. Each of these states corresponds to the electron in the hydrogen atom being in an 'orbit' whose radius rises through the quantum number n. The lowest permitted value of n is 1; since the electron is as close to the nucleus as possible, the energy of the system has its minimum (most negative) value. This is the "normal" (most stable) state of the hydrogen atom, and is termed the ground state. 

If a hydrogen atom absorbs radiation whose energy matches to the dissimilarity between that of n=1 and several higher values of n, then the atom is thought to be in an excited state. Excited states are unbalanced and rapidly decay to the ground state, but not always in a single step. For instance, if the electron is at first supported to the n = 3 state, it can decompose either to the ground state or to the n = 2 state, that then decays to n = 1. Therefore, this single n = 1→3 excitation can consequence in the 3 emission lines depicted in Figure, analogous to n = 3→1, n = 3→2, and n = 2→1. 

If, instead, sufficient energy is supplied to the atom to entirely eliminate the electron, we end up having a hydrogen ion and an electron. When such 2 particles recombine (H+ + e- → H), the electron can at first discover itself in a state analogous to any value of  n, leading to the emission of many lines.

The lines of the hydrogen spectrum can be organised into different series according to the value of n at which the emission terminates (or at which absorption originates.) The 1st few series are named after their founders. The most familiar (and 1st -observed) of such is the Balmer series, which lies generally in the visible region of the spectrum.

The Lyman lines are in the ultraviolet, while the other series lie in the infrared. The lines in each series crowd mutually as they converge toward the series limit that communicates to ionisation of the atom and is examined at the starting of the continuum emission. 

2183_Line Series in the Hydrogen Spectrum.jpg

Fig: Line Series in the Hydrogen Spectrum

Table: Description of the Line Series of the Hydrogen Spectrum

504_Description of the Line Series.jpg

The Bohr Theory accounts for the hydrogen spectrum in the given ways:

When hydrogen atoms are excited, their electrons engage orbitals having higher energies. 

When an electron goes back to a more stable orbit, it releases a photon of energy analogous to the energy difference between the orbits. 

The conversion back to the ground state can take place directly or stepwise, yielding a single photon or several photons. The various spectral series correspond to transitions between higher orbits and those having a given value of n. It is customary to refer to the integer n as a quantum number.

The Bohr Theory can be applied through equivalent achievement to "hydrogen-like atoms" that is, ions enclosing only 1 electron (He+, Li2+ and so on.). The expression for the energy of the electron in the nth orbit for such ions is following as:

Where Z symbolizes the atomic number.

Shortcomings of the Bohr Theory 

1. The Bohr Theory can't clarify the spectra of atoms enclosing more than 1 electron.

2. Even for the atoms through one electron, the theory doesn't expect the relative intensities of the lines or the dividing of the lines examined when the atoms are excited in a magnetic field (the Zeeman Effect). Even in the absence of outside fields, the spectral lines were established to be more compounds when examined through high resolution equipments. (The theory couldn't clarify the fine features of the spectra).

3. The theory ignores the wave nature of the electron.

4. It violates the Heisenberg's Uncertainty Principle - Bohr claims it is probable to know accurately the position and study the motion of the electron at the similar time.

5. It regards the electron as being stationary, through a precise position and distance from the nucleus.

6. It doesn't clarify molecular bonds.

7. It doesn't calculate the relative intensities of spectral lines.

8. The Bohr model doesn't clarify fine structure and hyperfine structure in spectral lines. 

Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)

Expand your confidence, grow study skills and improve your grades.

Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.

Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with an expert at http://www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology.  Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.

Free to know our price and packages for online chemistry tutoring. Chat with us or submit request at info@tutorsglobe.com