Classwork Series and Exercises {Physics – SS3}: Model Of Atoms

Physics SS3 Week 3

Topic: MODEL OF ATOMS

Thompson Rutherford Model

Modern atomic theory provides a reasonably satisfactory explanation of the properties of matter, the mechanisms of chemical change and the interaction of matter and energy. Such a theory emerged from the synthesis of the work of several scientists, only a few of which will be discussed here.

John Dalton (1766-1844) is generally credited as the father of the atomic theory but the early Greek philosophers were the originators of the concept of atoms. They taught that matter is composed of atom and is therefore finitely divisible, John Dalton considered the atom as constituting the simplest component of matter. He viewed the atom as ‘indestructible’, tiny hard spheres. The discovery of radioactivity by Henry Becquerel (1891 showed that atoms are complex rather than ‘indivisible’ or ‘indestructible’ but can disintegrate forming atom of different elements. The discovery of cathode rays in electric discharge tubes (1895) by William Crookes revealed that negatively charged electrons were components of the atom.

By 1900, it was already established that matter consists of atom but nothing was known about the structure of the atom. It was only known that the atoms contain electrons but that on the whole the atom was electrically neutral. This neutrality means that there must exist within the atom enough positively charged components to balance the negatively charged electrons. This led Sir J. J. Thomson the English Physicist, to propose an atomic model which visualized the atom as a homogeneous sphere of positive charge inside of which are embedded negatively charged electrons as shown below

J. J. Thomson also determined the ratio of the charge to mass, e/m, of electrons, and found e/m to be identical for all cathode-ray particles, irrespective of the kind of gas the in the tube or the metal the electrodes are made of.

Rutherford Model – the Nuclear Idea and the Planetary Model

Ernest Rutherford (1911) and his co-workers performed experiments a beam of positively charged alpha (α) particles was directed at a pin sheet of a metal foil. It was found that most of the alpha-particles passed through the foil without deflection as if the foil were mostly empty space. Only a few of them were diverted from their paths. Some of these few actually rebounded backwards.

The scattering of alpha-particle by the metal foil was explained as a repulsion from a heavy positively charged nucleus present at the centre of the atom of the metal foil. This follows because an abrupt change in path (as noted for a few α-particles) of a relatively heavy and positively charged α-particle can result only from its hitting or from its close approach to another particle (the nucleus) with a highly concentrated, positive charge. All these contradicted Thomson’s atomic model which supposed that the distribution of the charges was diffuse. Hence Rutherford proposed his model of the atom.

Rutherford proposed a planetary model of the atom which suggested that the atom consists of a positively charged heavy core called the nucleus which most of the mass of the atom was concentrated. Around this nucleus negatively charged electron circle in orbits much as planets move around the sun. Each nucleus must be surrounded by a number of electrons necessary to produce an electrically neutral atom.

This model was a major step toward how we view the atom today. It however had two problems. According to Newtonian Physics, such an atom as Rutherford’s would collapse by spiraling into the nucleus, since there is an attractive force between the oppositely charged nucleus and electrons. Further experiments indicated that charged moving in a field of opposite charge lose energy by emitting radiation. But atoms in their normal state neither collapsed nor emitted radiation.

Thus the two main difficulties of the Rutherford model are these:

1. It predicts that light of a continuous range of frequencies will be emitted, whereas experiment shows line spectra instead of continuous spectra.

2. It predicts that atoms are unstable – electrons quickly spiral into the nucleus – but we know that atoms in general are stable, since the matter around is stable.

Clearly Rutherford’s model was not sufficient to explain experimental observations. Some sort of modification was needed and this was provided by Neils Bohr.

Assumption of Bohr’s theory

In 1913 Niels Henrik Bohr published his new theory of the atoms constitution. Just like Rutherford he assumed that electrons rotate around the nucleus. But had the three completely new ideas:

1. There are some orbits called by him the stationery ones, where the moving electrons don’t emit energy.

2. Each emission or absorption of radiation energy represents the electron transition from one stationery orbit to another. The radiation emitted during such transition is homogeneous and its frequency is given by the formula:

where h is the Planck constant, E_n and E_l are the energies in the two stationary states.

3. The laws of mechanics describe the dynamic equilibrium of electrons in stationery states but do not describe the situation of the electron transition from one stationery orbit to another.

Let’s now think what each postulate means:

The first one says that electrons can’t move on unlimited orbits around the nucleus. Only some orbits are permissible. Electrons moving on them don’t lose energy for radiation. The postulate was in complete disagreement with other theories, and especially with the Maxwell theory of electromagnetism. Bohr formulated the postulate ad hoc. He didn’t know what it might come from. But he was of the opinion that to properly understand the nature of the atom one has to accept his idea. The second postulate says that in an atom an electron can change orbits. On each orbit the electron has some defined energy. The energy of the electron is different on different orbits. The bigger the orbit is, the bigger the energy is. If the electron change a higher orbit into a lower one then it emits a quant of energy that is the same as the difference of energy of the higher and lower orbit. To change a lower orbit into a higher one the electron has to absorb an adequate quant of energy. The quant of energy is proportional to the frequency of the emitted radiation. The second postulate explains why the atom emit radiation of strictly defined wavelengths.

The third postulate is in complete disagreement with the classic theory. According to that postulate the laws of mechanics can only describe electrons moving on stationary orbits and not while changing their orbits.

The Electron-Cloud Model

The model visualizes the atom as consisting of a tiny nucleus of radius of the order of 10^-15m. The electron is visualized as being in rapid motion within a relatively large region around the nucleus, but spending most of its time in certain high-probability regions. Thus the electron is not considered as a ball revolving around nucleus but as a particle or wave with a specified energy having only a certain probability of being in are given region in the space outside the nucleus. The electron is visualized as spread out around the nucleus in a sort of electron-cloud. Some chemists prefer to consider the electron in terms of a cloud of negative charges (electron cloud), with a cloud being dense in regions of high electron probability and more diffuse in regions of low probability.

This model is therefore known as the electron-cloud model. Most of the time, but not always, the electron will be located inside spherical outline. In other words, the probability of finding the electron inside the spherical bonding is high. The probability then decreases rapidly as the distance of the thin shell from the nucleus increases.

Protons, Neutrons and Isotope

In considering the atom as made up of a tiny but massive nucleus at the centre and outside the nucleus is a cloud of electrons which move in wave-like orbits or shells around the massive nucleus . The nucleus consists of protons which carry positive charges and neutrons which carry negative charges. The proton and the neutron together constitute the nucleon. Practically all the mass of an atom is concentrated in the central nucleus. The protons, neutrons and electrons are the fundamental subatomic particles of the atom.

The electron is the lightest particle of an atom, with a mass (m_e) of 9.1 x 10^-31 kg and an electronic charge e^– = 1.6 x 10^-19 C.

The proton has a mass of 1.67 x 10^-27 kg which is over 1836 times heavier than the mass of an electron. It carries a positive charge, e⁺ = 1.6 x 10^-19 C (i.e. e⁺ = e^– = 1.6 x 10^-19 C). There are the same number of protons in the atoms of a given element but different number of protons in the atoms of different elements. For example, there is only one proton in a hydrogen atom, but eleven proton in a sodium atom. In a neutral atom, the number of proton equals the number of electrons. The neutron has the same mass as the protons but it carries no charge.

We denote the atom of an element X by ^A_ZX where A is the mass number and Z is its atomic number.

The atomic number or proton number (Z) is the number of proton in the nucleus of an element. The mass number of Nucleon number (A) is the total number of protons and neutrons in an atom of an element. Thus the number of neutrons in the atom of an element. Thus the number of neutrons in the atom of an element equals the difference between the mass number and the atomic number (i.e. A-Z). The carbon atom denoted by ¹²₆C has 6 protons and 6 neutrons and a mass number of 12; the nitrogen atom denoted by ¹⁴₇N has 7 protons, and 7 neutrons and a mass number of 14. Since a neutral atom has the same number of electrons as the number of protons, ¹²₆C has 6 protons and 6 electrons.

An important question to consider is if all atoms are composed of these same components, why do different atoms have different chemical properties? The answer lies in the number and arrangement of the electrons. The electrons comprise most of the atomic value and thus are the parts that ‘intermingle’ when atoms combine to form molecules. Therefore the number of electrons possessed by a given atom greatly affects its ability to interact with other atoms.

The properties of the elements are periodic functions of their atomic number. When arranged in order of increasing atomic numbers, the elements with similar chemical properties recur at definite intervals, i.e. periodically. In regard to the electronic structure of electronic configuration (i.e. the arrangement of electrons in shells around the nucleus), this suggests a periodicity in the number of electrons in the outer shells of the atoms of the elements. The electrons in the outermost shell or shells of an atom are called valence electrons. These valence electrons are largely responsible for the chemical behavior of the atom of an element. If elements having the same number of valence electrons are grouped together, the elements falling within each group have similar chemical properties. Thus we note that atomic mass, atomic number, valence and periodicity, all indicate particularity of matter.

Isotopes are atoms of the same elements which have the same atomic number (Z) but different mass number. Isotopes are thus atoms with the same number of protons but different number of neutrons. Isotopes have similar chemical properties because they have the same number of electrons round the nucleus. Chemical combination is due to an exchange of outer or valence electrons between elements.

In nature, elements are usually found as a mixture of isotopes. For example, two naturally occurring isotopes of chlorine are

i. ³⁵₁₇CI (17 protons, 17 electrons, 18 neutrons)

ii. ³⁷₁₇CI (17 protons, 17 electrons, 20 neutrons)

For Carbon we have:

i. ¹²₆C (6 protons, 6 electrons, 6 neutrons)

ii. ¹³₆C (17 protons, 6 electrons, 7 neutrons)

For Oxygen we have:

i. ¹⁶₈O (8 protons, 8 electrons, 8 neutrons)

ii. ¹⁷₈O (8 protons, 8 electrons, 9 neutrons)

iii. ¹⁸₈O (8 protons, 8 electrons, 10 neutrons)

For Uranium we have:

i. ²³⁸₉₂U (92 protons, 92 electrons, 146 neutrons)

ii. ²³⁵₉₂U (92 protons, 92 electrons, 143 neutrons)

iii. ²³⁴₉₂U (92 protons, 92 electrons, 142 neutrons)

Questions

1. Which of the following statements is not correct? Isotopes of an element have

A. the same number of electric charges on the nucleus B. the same chemical properties C. different nucleon numbers   D. different atomic mass

2. Which of the following representations is correct for an atom X with 28 electrons and 30 neutrons?

A. ³⁰₂₈X B. ²⁸₃₀X C. ⁵⁸₃₀XD. ⁵⁸₂₈X

3. Which of the following statements are correct?

I The neutron has no charge II The electron is lighter than the proton III The proton is positively charged IV The algebraic sum of the charges on the protons and the charges on the neutrons in a neutral atom is zero

A. I, II, III, IV B. I, II, III only C. I, III and IV only D. II and IV only

4. Which of the following particles determine the mass of an atom?

A. Protons and neutrons B. Neutrons only C. Protons and electrons D. Neutrons and electrons

5. Which of the following names is not associated with models of the atom

A. Neils Bohr B. Ernest Rutherford C. J. J. Thomson D. Isaac Newton

Answers

1. C 2. D 3. A 4. A 5. D