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2539-2542
This is the reason why the Bohr’s model with its planet-like electron is not applicable to many electron atoms 5 Bohr laid the foundation of the quantum theory by postulating specific orbits in which electrons do not radiate Bohr’s model include only one quantum number n
9
2540-2543
5 Bohr laid the foundation of the quantum theory by postulating specific orbits in which electrons do not radiate Bohr’s model include only one quantum number n The new theory called quantum mechanics supportes Bohr’s postulate
9
2541-2544
Bohr laid the foundation of the quantum theory by postulating specific orbits in which electrons do not radiate Bohr’s model include only one quantum number n The new theory called quantum mechanics supportes Bohr’s postulate However in quantum mechanics (more generally accepted), a given energy level may not correspond to just one quantum state
9
2542-2545
Bohr’s model include only one quantum number n The new theory called quantum mechanics supportes Bohr’s postulate However in quantum mechanics (more generally accepted), a given energy level may not correspond to just one quantum state For example, a state is characterised by four quantum numbers (n, l, m, and s), but for a pure Coulomb potential (as in hydrogen atom) the energy depends only on n
9
2543-2546
The new theory called quantum mechanics supportes Bohr’s postulate However in quantum mechanics (more generally accepted), a given energy level may not correspond to just one quantum state For example, a state is characterised by four quantum numbers (n, l, m, and s), but for a pure Coulomb potential (as in hydrogen atom) the energy depends only on n 6
9
2544-2547
However in quantum mechanics (more generally accepted), a given energy level may not correspond to just one quantum state For example, a state is characterised by four quantum numbers (n, l, m, and s), but for a pure Coulomb potential (as in hydrogen atom) the energy depends only on n 6 In Bohr model, contrary to ordinary classical expectation, the frequency of revolution of an electron in its orbit is not connected to the frequency of spectral line
9
2545-2548
For example, a state is characterised by four quantum numbers (n, l, m, and s), but for a pure Coulomb potential (as in hydrogen atom) the energy depends only on n 6 In Bohr model, contrary to ordinary classical expectation, the frequency of revolution of an electron in its orbit is not connected to the frequency of spectral line The later is the difference between two orbital energies divided by h
9
2546-2549
6 In Bohr model, contrary to ordinary classical expectation, the frequency of revolution of an electron in its orbit is not connected to the frequency of spectral line The later is the difference between two orbital energies divided by h For transitions between large quantum numbers (n to n – 1, n very large), however, the two coincide as expected
9
2547-2550
In Bohr model, contrary to ordinary classical expectation, the frequency of revolution of an electron in its orbit is not connected to the frequency of spectral line The later is the difference between two orbital energies divided by h For transitions between large quantum numbers (n to n – 1, n very large), however, the two coincide as expected 7
9
2548-2551
The later is the difference between two orbital energies divided by h For transitions between large quantum numbers (n to n – 1, n very large), however, the two coincide as expected 7 Bohr’s semiclassical model based on some aspects of classical physics and some aspects of modern physics also does not provide a true picture of the simplest hydrogenic atoms
9
2549-2552
For transitions between large quantum numbers (n to n – 1, n very large), however, the two coincide as expected 7 Bohr’s semiclassical model based on some aspects of classical physics and some aspects of modern physics also does not provide a true picture of the simplest hydrogenic atoms The true picture is quantum mechanical affair which differs from Bohr model in a number of fundamental ways
9
2550-2553
7 Bohr’s semiclassical model based on some aspects of classical physics and some aspects of modern physics also does not provide a true picture of the simplest hydrogenic atoms The true picture is quantum mechanical affair which differs from Bohr model in a number of fundamental ways But then if the Bohr model is not strictly correct, why do we bother about it
9
2551-2554
Bohr’s semiclassical model based on some aspects of classical physics and some aspects of modern physics also does not provide a true picture of the simplest hydrogenic atoms The true picture is quantum mechanical affair which differs from Bohr model in a number of fundamental ways But then if the Bohr model is not strictly correct, why do we bother about it The reasons which make Bohr’s model still useful are: Rationalised 2023-24 305 Atoms (i) The model is based on just three postulates but accounts for almost all the general features of the hydrogen spectrum
9
2552-2555
The true picture is quantum mechanical affair which differs from Bohr model in a number of fundamental ways But then if the Bohr model is not strictly correct, why do we bother about it The reasons which make Bohr’s model still useful are: Rationalised 2023-24 305 Atoms (i) The model is based on just three postulates but accounts for almost all the general features of the hydrogen spectrum (ii) The model incorporates many of the concepts we have learnt in classical physics
9
2553-2556
But then if the Bohr model is not strictly correct, why do we bother about it The reasons which make Bohr’s model still useful are: Rationalised 2023-24 305 Atoms (i) The model is based on just three postulates but accounts for almost all the general features of the hydrogen spectrum (ii) The model incorporates many of the concepts we have learnt in classical physics (iii) The model demonstrates how a theoretical physicist occasionally must quite literally ignore certain problems of approach in hopes of being able to make some predictions
9
2554-2557
The reasons which make Bohr’s model still useful are: Rationalised 2023-24 305 Atoms (i) The model is based on just three postulates but accounts for almost all the general features of the hydrogen spectrum (ii) The model incorporates many of the concepts we have learnt in classical physics (iii) The model demonstrates how a theoretical physicist occasionally must quite literally ignore certain problems of approach in hopes of being able to make some predictions If the predictions of the theory or model agree with experiment, a theoretician then must somehow hope to explain away or rationalise the problems that were ignored along the way
9
2555-2558
(ii) The model incorporates many of the concepts we have learnt in classical physics (iii) The model demonstrates how a theoretical physicist occasionally must quite literally ignore certain problems of approach in hopes of being able to make some predictions If the predictions of the theory or model agree with experiment, a theoretician then must somehow hope to explain away or rationalise the problems that were ignored along the way EXERCISES 12
9
2556-2559
(iii) The model demonstrates how a theoretical physicist occasionally must quite literally ignore certain problems of approach in hopes of being able to make some predictions If the predictions of the theory or model agree with experiment, a theoretician then must somehow hope to explain away or rationalise the problems that were ignored along the way EXERCISES 12 1 Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is
9
2557-2560
If the predictions of the theory or model agree with experiment, a theoretician then must somehow hope to explain away or rationalise the problems that were ignored along the way EXERCISES 12 1 Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is the atomic size in Rutherford’s model
9
2558-2561
EXERCISES 12 1 Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is the atomic size in Rutherford’s model (much greater than/no different from/much less than
9
2559-2562
1 Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is the atomic size in Rutherford’s model (much greater than/no different from/much less than ) (b) In the ground state of
9
2560-2563
the atomic size in Rutherford’s model (much greater than/no different from/much less than ) (b) In the ground state of electrons are in stable equilibrium, while in
9
2561-2564
(much greater than/no different from/much less than ) (b) In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force
9
2562-2565
) (b) In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force (Thomson’s model/ Rutherford’s model
9
2563-2566
electrons are in stable equilibrium, while in electrons always experience a net force (Thomson’s model/ Rutherford’s model ) (c) A classical atom based on
9
2564-2567
electrons always experience a net force (Thomson’s model/ Rutherford’s model ) (c) A classical atom based on is doomed to collapse
9
2565-2568
(Thomson’s model/ Rutherford’s model ) (c) A classical atom based on is doomed to collapse (Thomson’s model/ Rutherford’s model
9
2566-2569
) (c) A classical atom based on is doomed to collapse (Thomson’s model/ Rutherford’s model ) (d) An atom has a nearly continuous mass distribution in a
9
2567-2570
is doomed to collapse (Thomson’s model/ Rutherford’s model ) (d) An atom has a nearly continuous mass distribution in a but has a highly non-uniform mass distribution in
9
2568-2571
(Thomson’s model/ Rutherford’s model ) (d) An atom has a nearly continuous mass distribution in a but has a highly non-uniform mass distribution in (Thomson’s model/ Rutherford’s model
9
2569-2572
) (d) An atom has a nearly continuous mass distribution in a but has a highly non-uniform mass distribution in (Thomson’s model/ Rutherford’s model ) (e) The positively charged part of the atom possesses most of the mass in
9
2570-2573
but has a highly non-uniform mass distribution in (Thomson’s model/ Rutherford’s model ) (e) The positively charged part of the atom possesses most of the mass in (Rutherford’s model/both the models
9
2571-2574
(Thomson’s model/ Rutherford’s model ) (e) The positively charged part of the atom possesses most of the mass in (Rutherford’s model/both the models ) 12
9
2572-2575
) (e) The positively charged part of the atom possesses most of the mass in (Rutherford’s model/both the models ) 12 2 Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil
9
2573-2576
(Rutherford’s model/both the models ) 12 2 Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil (Hydrogen is a solid at temperatures below 14 K
9
2574-2577
) 12 2 Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil (Hydrogen is a solid at temperatures below 14 K ) What results do you expect
9
2575-2578
2 Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil (Hydrogen is a solid at temperatures below 14 K ) What results do you expect 12
9
2576-2579
(Hydrogen is a solid at temperatures below 14 K ) What results do you expect 12 3 A difference of 2
9
2577-2580
) What results do you expect 12 3 A difference of 2 3 eV separates two energy levels in an atom
9
2578-2581
12 3 A difference of 2 3 eV separates two energy levels in an atom What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level
9
2579-2582
3 A difference of 2 3 eV separates two energy levels in an atom What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level 12
9
2580-2583
3 eV separates two energy levels in an atom What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level 12 4 The ground state energy of hydrogen atom is –13
9
2581-2584
What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level 12 4 The ground state energy of hydrogen atom is –13 6 eV
9
2582-2585
12 4 The ground state energy of hydrogen atom is –13 6 eV What are the kinetic and potential energies of the electron in this state
9
2583-2586
4 The ground state energy of hydrogen atom is –13 6 eV What are the kinetic and potential energies of the electron in this state 12
9
2584-2587
6 eV What are the kinetic and potential energies of the electron in this state 12 5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level
9
2585-2588
What are the kinetic and potential energies of the electron in this state 12 5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level Determine the wavelength and frequency of photon
9
2586-2589
12 5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level Determine the wavelength and frequency of photon 12
9
2587-2590
5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level Determine the wavelength and frequency of photon 12 6 (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels
9
2588-2591
Determine the wavelength and frequency of photon 12 6 (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels (b) Calculate the orbital period in each of these levels
9
2589-2592
12 6 (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels (b) Calculate the orbital period in each of these levels 12
9
2590-2593
6 (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels (b) Calculate the orbital period in each of these levels 12 7 The radius of the innermost electron orbit of a hydrogen atom is 5
9
2591-2594
(b) Calculate the orbital period in each of these levels 12 7 The radius of the innermost electron orbit of a hydrogen atom is 5 3×10–11 m
9
2592-2595
12 7 The radius of the innermost electron orbit of a hydrogen atom is 5 3×10–11 m What are the radii of the n = 2 and n =3 orbits
9
2593-2596
7 The radius of the innermost electron orbit of a hydrogen atom is 5 3×10–11 m What are the radii of the n = 2 and n =3 orbits 12
9
2594-2597
3×10–11 m What are the radii of the n = 2 and n =3 orbits 12 8 A 12
9
2595-2598
What are the radii of the n = 2 and n =3 orbits 12 8 A 12 5 eV electron beam is used to bombard gaseous hydrogen at room temperature
9
2596-2599
12 8 A 12 5 eV electron beam is used to bombard gaseous hydrogen at room temperature What series of wavelengths will be emitted
9
2597-2600
8 A 12 5 eV electron beam is used to bombard gaseous hydrogen at room temperature What series of wavelengths will be emitted 12
9
2598-2601
5 eV electron beam is used to bombard gaseous hydrogen at room temperature What series of wavelengths will be emitted 12 9 In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1
9
2599-2602
What series of wavelengths will be emitted 12 9 In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1 5 × 1011 m with orbital speed 3 × 104 m/s
9
2600-2603
12 9 In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1 5 × 1011 m with orbital speed 3 × 104 m/s (Mass of earth = 6
9
2601-2604
9 In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1 5 × 1011 m with orbital speed 3 × 104 m/s (Mass of earth = 6 0 × 1024 kg
9
2602-2605
5 × 1011 m with orbital speed 3 × 104 m/s (Mass of earth = 6 0 × 1024 kg ) Rationalised 2023-24 Physics 306 13
9
2603-2606
(Mass of earth = 6 0 × 1024 kg ) Rationalised 2023-24 Physics 306 13 1 INTRODUCTION In the previous chapter, we have learnt that in every atom, the positive charge and mass are densely concentrated at the centre of the atom forming its nucleus
9
2604-2607
0 × 1024 kg ) Rationalised 2023-24 Physics 306 13 1 INTRODUCTION In the previous chapter, we have learnt that in every atom, the positive charge and mass are densely concentrated at the centre of the atom forming its nucleus The overall dimensions of a nucleus are much smaller than those of an atom
9
2605-2608
) Rationalised 2023-24 Physics 306 13 1 INTRODUCTION In the previous chapter, we have learnt that in every atom, the positive charge and mass are densely concentrated at the centre of the atom forming its nucleus The overall dimensions of a nucleus are much smaller than those of an atom Experiments on scattering of a-particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about 104
9
2606-2609
1 INTRODUCTION In the previous chapter, we have learnt that in every atom, the positive charge and mass are densely concentrated at the centre of the atom forming its nucleus The overall dimensions of a nucleus are much smaller than those of an atom Experiments on scattering of a-particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about 104 This means the volume of a nucleus is about 10–12 times the volume of the atom
9
2607-2610
The overall dimensions of a nucleus are much smaller than those of an atom Experiments on scattering of a-particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about 104 This means the volume of a nucleus is about 10–12 times the volume of the atom In other words, an atom is almost empty
9
2608-2611
Experiments on scattering of a-particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about 104 This means the volume of a nucleus is about 10–12 times the volume of the atom In other words, an atom is almost empty If an atom is enlarged to the size of a classroom, the nucleus would be of the size of pinhead
9
2609-2612
This means the volume of a nucleus is about 10–12 times the volume of the atom In other words, an atom is almost empty If an atom is enlarged to the size of a classroom, the nucleus would be of the size of pinhead Nevertheless, the nucleus contains most (more than 99
9
2610-2613
In other words, an atom is almost empty If an atom is enlarged to the size of a classroom, the nucleus would be of the size of pinhead Nevertheless, the nucleus contains most (more than 99 9%) of the mass of an atom
9
2611-2614
If an atom is enlarged to the size of a classroom, the nucleus would be of the size of pinhead Nevertheless, the nucleus contains most (more than 99 9%) of the mass of an atom Does the nucleus have a structure, just as the atom does
9
2612-2615
Nevertheless, the nucleus contains most (more than 99 9%) of the mass of an atom Does the nucleus have a structure, just as the atom does If so, what are the constituents of the nucleus
9
2613-2616
9%) of the mass of an atom Does the nucleus have a structure, just as the atom does If so, what are the constituents of the nucleus How are these held together
9
2614-2617
Does the nucleus have a structure, just as the atom does If so, what are the constituents of the nucleus How are these held together In this chapter, we shall look for answers to such questions
9
2615-2618
If so, what are the constituents of the nucleus How are these held together In this chapter, we shall look for answers to such questions We shall discuss various properties of nuclei such as their size, mass and stability, and also associated nuclear phenomena such as radioactivity, fission and fusion
9
2616-2619
How are these held together In this chapter, we shall look for answers to such questions We shall discuss various properties of nuclei such as their size, mass and stability, and also associated nuclear phenomena such as radioactivity, fission and fusion 13
9
2617-2620
In this chapter, we shall look for answers to such questions We shall discuss various properties of nuclei such as their size, mass and stability, and also associated nuclear phenomena such as radioactivity, fission and fusion 13 2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS The mass of an atom is very small, compared to a kilogram; for example, the mass of a carbon atom, 12C, is 1
9
2618-2621
We shall discuss various properties of nuclei such as their size, mass and stability, and also associated nuclear phenomena such as radioactivity, fission and fusion 13 2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS The mass of an atom is very small, compared to a kilogram; for example, the mass of a carbon atom, 12C, is 1 992647 × 10–26 kg
9
2619-2622
13 2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS The mass of an atom is very small, compared to a kilogram; for example, the mass of a carbon atom, 12C, is 1 992647 × 10–26 kg Kilogram is not a very convenient unit to measure such small quantities
9
2620-2623
2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS The mass of an atom is very small, compared to a kilogram; for example, the mass of a carbon atom, 12C, is 1 992647 × 10–26 kg Kilogram is not a very convenient unit to measure such small quantities Therefore, a Chapter Thirteen NUCLEI Rationalised 2023-24 307 Nuclei different mass unit is used for expressing atomic masses
9
2621-2624
992647 × 10–26 kg Kilogram is not a very convenient unit to measure such small quantities Therefore, a Chapter Thirteen NUCLEI Rationalised 2023-24 307 Nuclei different mass unit is used for expressing atomic masses This unit is the atomic mass unit (u), defined as 1/12th of the mass of the carbon (12C) atom
9
2622-2625
Kilogram is not a very convenient unit to measure such small quantities Therefore, a Chapter Thirteen NUCLEI Rationalised 2023-24 307 Nuclei different mass unit is used for expressing atomic masses This unit is the atomic mass unit (u), defined as 1/12th of the mass of the carbon (12C) atom According to this definition mass of one 12 C atom 1u = 12 26 1
9
2623-2626
Therefore, a Chapter Thirteen NUCLEI Rationalised 2023-24 307 Nuclei different mass unit is used for expressing atomic masses This unit is the atomic mass unit (u), defined as 1/12th of the mass of the carbon (12C) atom According to this definition mass of one 12 C atom 1u = 12 26 1 992647 10 kg 12 − × = 27 1
9
2624-2627
This unit is the atomic mass unit (u), defined as 1/12th of the mass of the carbon (12C) atom According to this definition mass of one 12 C atom 1u = 12 26 1 992647 10 kg 12 − × = 27 1 660539 10 kg − = × (13
9
2625-2628
According to this definition mass of one 12 C atom 1u = 12 26 1 992647 10 kg 12 − × = 27 1 660539 10 kg − = × (13 1) The atomic masses of various elements expressed in atomic mass unit (u) are close to being integral multiples of the mass of a hydrogen atom
9
2626-2629
992647 10 kg 12 − × = 27 1 660539 10 kg − = × (13 1) The atomic masses of various elements expressed in atomic mass unit (u) are close to being integral multiples of the mass of a hydrogen atom There are, however, many striking exceptions to this rule
9
2627-2630
660539 10 kg − = × (13 1) The atomic masses of various elements expressed in atomic mass unit (u) are close to being integral multiples of the mass of a hydrogen atom There are, however, many striking exceptions to this rule For example, the atomic mass of chlorine atom is 35
9
2628-2631
1) The atomic masses of various elements expressed in atomic mass unit (u) are close to being integral multiples of the mass of a hydrogen atom There are, however, many striking exceptions to this rule For example, the atomic mass of chlorine atom is 35 46 u
9
2629-2632
There are, however, many striking exceptions to this rule For example, the atomic mass of chlorine atom is 35 46 u Accurate measurement of atomic masses is carried out with a mass spectrometer, The measurement of atomic masses reveals the existence of different types of atoms of the same element, which exhibit the same chemical properties, but differ in mass
9
2630-2633
For example, the atomic mass of chlorine atom is 35 46 u Accurate measurement of atomic masses is carried out with a mass spectrometer, The measurement of atomic masses reveals the existence of different types of atoms of the same element, which exhibit the same chemical properties, but differ in mass Such atomic species of the same element differing in mass are called isotopes
9
2631-2634
46 u Accurate measurement of atomic masses is carried out with a mass spectrometer, The measurement of atomic masses reveals the existence of different types of atoms of the same element, which exhibit the same chemical properties, but differ in mass Such atomic species of the same element differing in mass are called isotopes (In Greek, isotope means the same place, i
9
2632-2635
Accurate measurement of atomic masses is carried out with a mass spectrometer, The measurement of atomic masses reveals the existence of different types of atoms of the same element, which exhibit the same chemical properties, but differ in mass Such atomic species of the same element differing in mass are called isotopes (In Greek, isotope means the same place, i e
9
2633-2636
Such atomic species of the same element differing in mass are called isotopes (In Greek, isotope means the same place, i e they occur in the same place in the periodic table of elements
9
2634-2637
(In Greek, isotope means the same place, i e they occur in the same place in the periodic table of elements ) It was found that practically every element consists of a mixture of several isotopes
9
2635-2638
e they occur in the same place in the periodic table of elements ) It was found that practically every element consists of a mixture of several isotopes The relative abundance of different isotopes differs from element to element
9
2636-2639
they occur in the same place in the periodic table of elements ) It was found that practically every element consists of a mixture of several isotopes The relative abundance of different isotopes differs from element to element Chlorine, for example, has two isotopes having masses 34
9
2637-2640
) It was found that practically every element consists of a mixture of several isotopes The relative abundance of different isotopes differs from element to element Chlorine, for example, has two isotopes having masses 34 98 u and 36
9
2638-2641
The relative abundance of different isotopes differs from element to element Chlorine, for example, has two isotopes having masses 34 98 u and 36 98 u, which are nearly integral multiples of the mass of a hydrogen atom