a-particles are actually helium atoms from which electrons have been removed. Each a-particle consists of a mass equal to about 4 times that of hydrogen atom and carries a positive charge of 2 units. It is represented by symbol .

If Thomson’s explanation were correct, a-particles would have been deflected at very small angles only

from a straight line path. But Rutherford found that maximum a-particles go straight, some get deflected at small angles, a few at large angles and in rare cases the deflection is 180° as shown in fig. 1.4. He hypothesised that deflection at 180° can arise only if an intense positive electric field is present inside atoms. Observations showed that a positive charge spread throughout a sphere of radius 10^-8 cm would be incapable of producing this field. Calculations showed that this radius should be of the order 10^-13 cm to account for scattering data. Based on these observations Rutherford presented following model for atom.

Þ        Atom consists of a nucleus which contains protons making it positively charged & mass being centered here in a small space of radius 10^-13 cm.

Þ        There is a lot of empty space around nucleus in which electrons are present. The total size of the atom is of radius 10^-8 cm.

Þ        Electrons can’t be stationary as they would be pulled by nucleus. Instead they are revolving around nucleus, the necessary centripetal force for revolutions is provided by attractive forces between nucleus & electrons

Bohr also argued the same that the electron  (being a charged particle) should also lose energy while moving in a circle (i.e. with an acceleration). As a result its orbit should become smaller and smaller and finally it should drop into the nucleus. But the fact is that atom is stable.

Niel’s Bohr supplied a solution to this problem by applying Planck’s quantum theory. Let us first study the Planck’s quantum theory.

Planck’s quantum theory (1901)

It states

Þ        Radiant energy is emitted or absorbed discontinuously in the form of tiny bundles of energy called Quanta.

Þ    Each quantum is associated with a definite amount of energy E which is proportional to frequency of radiation.

where,             h = Planck’s constant = 6.626 * 10^-34 Joule-sec.

v = Frequency of the light radiation

Þ        A body can emit or absorb radiations only in whole multiples of quantum i.e. E = nhv where
n = 1, 2, 3, …….

Bohr’s atomic model

The postulates of Bohr’s atomic theory stability of an atom are as follows

Electron revolves in only allowed stationary orbits. Energy of different stationary states vary. An electron can be excited from a lower state to higher state with the absorption of a quantum of energy, or can come down from a higher to lower state with emission of a radiation of energy (as shown in figure 1.5) equal to energy to quantum ΔE = E2 - E1 = hv. E2 & E1 are energies of the electron associated with stationary orbits.

The stability of the circular motion of an electron requires that the electrostatic force (due to the attraction between the nucleus and the electron) provides the necessary centrepetal force for the motion of electron.

where Z – atomic number

e – charge on electron

ε0 - permittivity of the charge in vaccum

r – distance between positive charge & electron

Angular momentum of electron is quantised i.e. electron can revolve only in those orbits where its angular momentum is an integral multiple of h/2Π.

where, v – velocity of electron

m – mass of electron

h – Planck’s constant

n = 1, 2, 3, …. are known as Principal quantum number.

COMMON RULES FOR COUNTING

SIGNIFICANT FIGURES

Following are some of the common rules for counting significant figures in a given expression :

P                 All zeros occurring between two non zero digits are significant. For example: x = 5008 has four significant figures. Again x = 7.0102 has five significant figures.

P                 All non zero digits are significant.

For example: x = 7284 has four significant figures. Again x = 457 has only three significant digits.

P                 All zeros on the right of the last non zero digit in the decimal part are significant. For example                      x = 0.00400 has three significant figures.

P                 e.g., x = 0.00800, x=1.00;  The zeros before 8 are not significant.  1.00 has three significant figures.

P                 In a number less than one, all zeros to the right of decimal point and to the left of a non zero digit are NOT significant.

P                 For example: x = 0.0088 has only two significant digits. Again x = 1.0088 has five significant figures.

P                 All zeros on the right of the last non-zero digit become significant, when they come from a measurement.

For example, suppose distance between two stations is measured to be 3850 m. It has four significant figures. The same distance can be expressed as 3.850×10⁵ cm. In all these expressions, number of significant figures continues to be four.

P                 All zeros on the right of non-zero digit are NOT significant.

For example, x = 7000 has only one significant figure. Again x = 848000 has three significant figures.

ROUNDING OFF

While rounding off measurements, we use the following rules by convention:

P     If the digit to be dropped is more than 5, then the preceding digit is raised by one.

For example, x = 6.87 is rounded off to 6.9. Again x = 12.78 is rounded off to 12.8 .

P     If the digit to be dropped is less than 5, then the preceding digit is left unchanged.

For example, x = 7.82 is rounded off to 7.8 . Again x = 3.94 is rounded off to 3.9 .

P     If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is raised by one.

For example, x = 16.351 is rounded off to 16.4. Again x = 6.758 is rounded off to 6.8 .

P     If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by one, if it is odd.

For example, x = 3.750 is rounded off to 3.8. Again x = 16.150 is rounded off to 16.2 .

If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is left unchanged, if it is even.

For example, x = 3.250 becomes 3.2 on rounding off, Again x = 12.650 becomes 12.6 on rounding off.

ARITHMENTICAL OPERATIONS WITH SIGNIFICANT FIGURES

(i) Addition and subtraction.

In addition or subtraction, the number of decimal places in the result should equal the smallest number of decimal places of terms in the operation. Suppose, in the measured values to be added or subtracted, the least number of significant digits after the decimal is N. Then in the sum or difference also, the number of significant digits after the decimal should be N.

For example, the sum of three measurements of length; 2.1 m, 1.78 m and 2.046 m is 5.926m, which is rounded off to 5.9 m (upto smallest number of decimal places).

In the subtraction of quantities of nearly equal magnitudes, accuracy is  almost destroyed. For example, if x = 42.87m and y = 12.86m, then

x – y = 12.87 – 12.86 = 0.01 m. The difference has only one significant figure, whereas x and y have four significant digits each.

(ii) Multiplication and Division

In multiplication and division, the number of significant figures in the product or in the quotient is the same as the smallest number of significant figures in any of the factors.

For example, suppose x = 3.8 and y = 0.125.  Therefore, xy = (3.8) (0.125) = 0.475. As least number of significant figures is 2 (in x = 3.8). Therefore, xy = 0.475 = 0.48 is rounded off to two significant figures.

Example

(i)      3.24 + 4.200018 + 5.0

= 12.440018≈  12.4

Here least number of significant digits after the decimal is one in 5.0. Same is the case with the sum

(ii)      6.21192 – 3.10   = 3.11192  ≈3.11

Here least number of significant digits after the decimal is two in 3.10. Same is the case with the difference.

Multiplication and division of measured values

ü     Suppose, in the measured values to be multiplied or divided, the least number of significant digits be N. Then in the product or quotient, the number of significant digits should be N.

Example

(i)   3.224 * 2.3 = 7.4152 ≈7.4

(ii)  46.64/2.3 =20.3=≈20

Here least number of significant digits is two in 2.3 and same should be the case with product or quotient

Þ  Change in the position of decimal point does not change the number of significant digits in the measured value.  For example, the number of significant digits both in 12.340 * 10² as well as 1234.0 is 5.

Þ The change in the units of measured value does not change the significant digits.

Rounding off a Digit

ü     We round off the number to obtain its value with a definite number of significant digits. Following are the rules for rounding off.

If the number lying to the right of cut off digits be

less than 5, then the cut off digit is retained as

such. However if it is more than 5, then the cut off

digit is increased by 1.

Example

Consider the number 324.1283. To round it off to 4 significant digits, we can write:

324.1283  ≈ 324.1. Again consider the number 324.1823. To round it off to 4 significant digits, we can write: 324.1823 ≈  324.2

Þ If the number to the right of cut off digit be 5, then we proceed as follows:

(a) Increase the cut off digit by 1 if it is odd.

(b) Retain the cut off digit as such if it is even

Example

324.1532  ≈324.2 and 324.2532  ≈324.2

Important

ü     While rounding off, the process should, in fact, be carried out from the last digit to the right. For example to round off 324.14821 to 4 significant digits, we should proceed as follows:

324.14821  ≈324.1482 ≈324.148 ≈324.15 ≈324.2

Þ In general no finally calculated value should have more significant figures than the least significant figures in the given data to be multiplied or divided. However, if multiple steps are involved, in the intermediate steps it is better to retain one significant figure more than the least number of significant figures in the given data.

Electrical discharge through partially evacuated tubes produced radiation. This radiation originated from near the negative electrode, known as the cathode (thus, these rays were termed cathode rays).

• The “rays” traveled towards, or were attracted to the positive electrode (anode)
• Not directly visible but could be detected by their ability to cause other materials to glow, or fluoresce
• Traveled in straight line
• Their path could be “bent” by the influence of magnetic or electrical fields
• A metal plate in the path of the “cathode rays” aquired a negative charge
• The “cathode rays” produced by cathodes of different materials appeared to have the same properties

These observations indicated that the cathode ray were composed of negatively charged particles (now known as electrons).

J.J. Thompson (1897) measured the charge to mass ratio for a stream of electrons (using a cathode ray tube apparatus) at 1.76 x 10⁸ coulombs/gram.

• Charged particle stream can be deflected by both an electric and by a magnetic field
• An electric field can be used to compensate for the magnetic deflection – the resulting beam thus behaves as if it were neutral
• The field needed to “neutralize” the magnetic field indicates the charge of the beam

Thompson determined the charge to mass ratio for the electron, but was not able to determine the mass of the electron.

However, from his data, if the charge of a single electron could be determined, then the mass of a single electron could also be determined.

Robert Millikan (1909) was able to successfully measure the charge on a single electron (the “Milliken oil drop experiment”). This value was determined to be 1.60 x 10^-19 coulombs.

Thus, the mass of a single electron was determined to be:

(1 gram/1.76 x 10⁸ coulombs)*(1.60 x 10^-19 coulombs) = 9.10 x 10^-28 grams

Note: the currently accepted value for the mass of the electron is 9.10939 x 10^{- 28} grams.

OBJECTIVE

Towards the end of the nineteenth century, it began to appear that the atom itself might be composed of even smaller particles. In 1833, Michael Faraday showed that there is a relationship between matter and electricity. This was the first major breakthrough to suggest that an atom was not a simple indivisible particle yet smaller but was made up of  particles. On the basis of Faraday’s work, Stoney proposed that units of electrical charge are associated with atoms. In 1891, he suggested that these units be called electrons. Electron is a Greek word meaning amber, a material which becomes electrically charged when rubbed with wool or silk.

It is now believed that the atom consists of several particles called sub-atomic particles like electron, proton, neutron, etc. the electron, the proton and the neutron are called Fundamental particles and are building blocks of the atoms about which we shall deal with in this chapter.

PRE-REQUISITE

Law of conservation of Mass

In a chemical reaction the weight of products is equal to the weight of reactants.

Law of definite proportions

If a compound is analysed from various sources, its elemental composition remains the same i.e., analysis of water from a river or ditch or pond either in India or in USA would always give H:O ratio as 2:1. (atom ratio)

Law of Multiple Proportions

Elements combine in simple whole number ratios to form various types of compounds e.g. The ratio of N:O is 1:1, 1:2 and 2:1 in NO, NO₂ and N₂O, respectively.

Atomic Number (Z)

The total number of protons present in the nucleus of an atom is called as atomic number of that atom.

Mass Number (A)

Total number of nucleons (protons + neutrons) in the nucleus of an atom is called it mass number.

Isotopes

Atoms with the same atomic number but different mass numbers are called isotopes of each other. For example the isotopes of hydrogen atom are: ₁H¹, ₁H², ₁H³.

Isobars

Atoms with same mass number but different atomic number are called as isobars of each other. For example ₁₅P³² and ₁₆S³² are isobars of each other.

Isotones

Atoms having the same number of neutrons but different number of protons are called isotones. For example ₆C¹⁴, ₈O¹⁶, ₇N¹⁵ are isotones as they all have 8 neutrons.

Isodiaphers

Atoms having the same value of (A – 2Z) but different value of A or Z are called isodiapheres. For example ₁₁Na²³, ₉F¹⁹, ₇N¹⁵ are isodiapheres as (A – 2Z) for all these three atoms is 1.

Nuclear Isomers

Nuclear isomers (isomeric nuclei) are the atoms with the same atomic number and same mass number but different radioactive properties are called nuclear isomers. This type of isomerism is due to the different energy states of the two isomeric nuclei. For example ₃₀Zn⁶⁹ and ₃₀Zn⁶⁹ are two atoms with their half life periods 13.8 hours and 57 minutes respectively.

Isoelectronic

Atoms, molecules or ions with same number of electrons are called isoelectronic. For example N₂, CO, CN^- are isoelctronic.