What are cathode rays?

A simple and convenient device used to study the conduction of electricity through gases is known as gas discharge tube. When the pressure reaches to around 0 . 01 mm of Hg , positive column disappears. At this time, a dark space is formed between anode and cathode which is often called Crookes dark space and the walls of the tube appear with green colour. At this stage, some invisible rays emanate from cathode called cathode rays, which are later found be a beam of electrons.

E M B I B E

Physics Standard 12 Vol II>Chapter -1 - Atomic and Nuclear Physics>EVALUATION>Q 9

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Earn 100

Discuss the gamma decay process with example.

Important Points to Remember in Chapter -1 - Atomic and Nuclear Physics from Tamil Nadu Board Physics Standard 12 Vol II Solutions

1. Thomson's model:

(i) Atom, as a whole, is electrically neutral and therefore contains equal amount of positive and negative charges.

(ii) In Thomson’s model, an atom is a spherical cloud of positive charges with electrons embedded in it.

2. Rutherford’s atomic model:

(i) In Rutherford’s model, most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus (typically one by ten thousand the size of an atom), and the electrons revolve around it.

(ii) Rutherford's model predicts that atoms are unstable because the accelerated electrons revolving around the nucleus must spiral into the nucleus. This contradicts the stability of matter.

(iii) It cannot explain the characteristic line spectra of atoms of different elements.

3. Spectral series:

The atomic hydrogen emits a line spectrum consisting of various series. The frequency of any line in a series can be expressed as
Lyman series: $f = R c (\frac{1}{1^{2}} - \frac{1}{n^{2}}); n = 2,3, 4, \dots$
Balmer series: $f = R c (\frac{1}{2^{2}} - \frac{1}{n^{2}}); n = 3,4, 5, \dots$
Paschen series: $f = R c (\frac{1}{3^{2}} - \frac{1}{n^{2}}); n = 4,5, 6, \dots$
Brackett series: $f = R c (\frac{1}{4^{2}} - \frac{1}{n^{2}}); n = 5,6, 7, \dots$
Pfund series: $f = R c (\frac{1}{5^{2}} - \frac{1}{n^{2}}); n = 6,7, 8, \dots$

4. Bohr's atomic model:

(i) Niel’s Bohr proposed a model for hydrogenic (single electron) atoms. He introduced three postulates and laid the foundations of quantum mechanics.

(ii) When an electron transits from higher energy level to lower energy level a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency of the emitted photon is then given by: $h v = E_{i} - E_{f}$ .

(iii) An atom absorbs radiation of the same frequency the atom emits, in which case the electron is transferred to an orbit with a higher value of $n$ . $E_{i} + h v = E_{f}$

(iv) For the electron revolving in a stationary orbit is $L = n h / 2 π$ where $n$ is an integer called a quantum number.

(v) In a hydrogen atom, an electron revolves in certain stable orbits (called stationary orbits) without the emission of radiant energy.

(vi) For a hydrogen atom radius of $n^{t h}$ energy level, $r_{n} = (\frac{n^{2}}{m}) {(\frac{h}{2 π})}^{2} \frac{4 π ε_{0}}{e^{2}}$

(vii) Energy of the electron in $n^{t h}$ energy level $E_{n} = - \frac{m e^{4}}{8 n^{2} ε_{0}^{2} h^{2}} = - 13.6 \frac{1}{n^{2}} e V$

(viii) Bohr’s model is applicable only to hydrogenic (single electron) atoms.

5. de Broglie's explanation of bohr's second postulate of quantisation:

de Broglie’s hypothesis that electrons have a wavelength $λ = h / m v$ gave an explanation for Bohr’s quantised orbits by bringing in the wave particle duality. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.

6. Atomic masses and composition of nucleus:

(i) An atom has a nucleus. The nucleus is positively charged. The radius of the nucleus is smaller than the radius of an atom by a factor of $10^{4}$ . More than $99.9 %$ mass of the atom is concentrated in the nucleus.

(ii) $1$ atomic mass unit $(1 u)$ is $1 / 12^{th}$ mass of one atom of $^{12} C$ , $1 u = 1.660563 \times 10^{- 27} k g$ .

(iii) The atomic number $Z$ is the number of protons in the atomic nucleus of an element. The mass number $A$ is the total number of protons and neutrons in the atomic nucleus; $A = Z + N$ ; Here $N$ denotes the number of neutrons in the nucleus.

(iv) A nuclear species or a nuclide is represented as $_{Z}^{A} X$ , where $X$ is the chemical symbol of the species.

(v) Nuclides with the same atomic number, but different neutron number are called isotopes. Nuclides with the same mass number are isobars and those with the same neutron number are isotones.

7. Size of the nucleus:

(i) Radii of nuclei $R = R_{0} A^{1 / 3}$ where $R_{0} = 1.2 f m$ and $A$ is mass number.

(ii) Nuclear density is independent of A. It is of the order of $10^{17} k g / m^{3}$ .

8. Nuclear force:

Neutrons and protons are bound in a nucleus by the short-range strong nuclear force. The nuclear force does not distinguish between neutron and proton.

9. Mass defect:

The nuclear mass M is always less than the total mass, of its constituents. The difference in mass of a nucleus and its constituents is called the mass defect. $Δ M = (Z m_{p} + (A - Z) m_{n}) - M$ .

10. Binding energy:

Binding energy is the energy released during the formation of nucleus, $Δ E_{b} = Δ M c^{2}$

11. Q-value:

The $Q$ -value of a nuclear process is the amount of energy released or absorbed during the nuclear process.

$Q =$ (sum of initial masses – sum of final masses) $c^{2}$

12. Radioactivity:

(i) Law of radioactive decay: $N (t) = N_{0} e^{- λ t}$ where $λ$ is the decay constant or disintegration constant.

(ii) The half-life $T_{1 / 2} = \frac{\ln 2}{λ}$

(iii) The mean life $T = \frac{1}{λ}$

13. Nuclear fusion and nuclear fission:

(i) In fission, a heavy nucleus like $_{92}^{235} U$ breaks into two smaller fragments, e.g., $_{92}^{235} U +_{0}^{1} n \to_{51}^{133} S b +_{41}^{99} N b + 4_{0}^{1} n$

(ii) In fusion, lighter nuclei combine to form a larger nucleus. Fusion of hydrogen nuclei into helium nuclei is the source of energy of all stars including our sun.

Learn and Prepare for any exam you want !

|

|

|

|

|

|

|

|