Structure of the Atom

Question 1

What are the two Bohr’s postulates for the atom?

Answer 1

1. Allowed or the permissible orbits for which the angular momentum of the electron is the integral multiple of reduced Planck’s constant. These are called stationary orbits.
2. An atoms radiates energy only when an electron jumps from a stationary orbit of higher energy to one of lower energy. The energy of the radiation is the difference in energies of the electron at two orbits.

Question 2

Derive the expression of Bohr’s stationary orbits’ radius and total energy of the electrons at that orbit.

Answer 2

Refer to the book for the answer.

Question 3

What are the considerations or the assumptions made to calculate Bohr’s orbit?

Answer 3

Charge of nucleus and electron.
Mass of nucleus and electron.
Mass of nucleus is far more than the mass of electron.
And, the radius of the orbit.

Question 4

Write the formula for Bohr’s radius and the Total energy of the nth Bohr’s orbit?

Answer 4

Refer to the book

Question 5

What was the Bohr’s interpretation of the Hydrogen spectrum?

Answer 5

Refer to the book

Question 6

What is Rydberg constant? Write its formula and where it came from? Also write its value in units.

Answer 6

Refer to the book for this

Question 7

Explain the spectral series of the hydrogen atom?

Answer 7

Refer to the book

Question 8

Write the value of total energy of the electron for the first four Bohr’s orbits?

Answer 8

for 1, -13.6 eV
for 2, -3.4 eV
for 3, - 1.51eV
for 4, -0.85 eV

Question 9

What is one electron volt? What is it’s value?

Answer 9

the energy gained by an electron when it has been accelerated by a potential difference of 1 volt.

The value = 1.602176634×10^(−19) J.

= charge of the electron * 1 volt

Question 10

Difference between the ionization potential and the excitation potential with an illustrative example.

Answer 10

Refer to the book

Question 11

Draw a well labelled schematic diagram of Frank and Hertz experiment and the graph obtained. Explain both.

Answer 11

Refer to the book

Question 12

What is the result of Frank and Hertz experiment?

Answer 12

This experiment shows in a very convincing way the existence of the discrete energy levels in atom.

Question 13

What does Frank and Hertz experiment show?

Answer 13

The energy lost by the electron in its inelastic collision with the mercury atoms reappears as a quantum of energy of the wavelength hc/E.

Question 14

How the collision is inelastic in Frank and Hertz experiment?

Question 15

What is the main drawback of Frank and Hertz experiments?

Answer 15

It cannot distinguish between excitation potential and ionization potential.

How though?

Question 16

Explain the role of three different voltages in Frank and Hertz experiment.

Answer 16

Refer to the book for the answer.

Question 17

Explain the graph of the Frank and Hertz experiment.

Answer 17

Refer to the book

Question 18

Write the four basic formula used in Sommerfeld’s Relativistic Atom Model.

Answer 18

Refer to the notes

Question 19

Write the two assumptions of the Sommerfeld’s Relativistic Atom Model.

Answer 19

1. The path of an electron orbiting around a nucleus is, in general, ellipse. The circular orbits are a special case of this.
   2.The mass of the electron orbiting around the nucleus varies relativistically with its velocity.

Question 20

Write the equation of an ellipse in polar coordinates.

Answer 20

Refer to the book

Question 21

Write the standard integral and its integrated value, that is involved in mathematic analysis of Sommerfeld’s Relativistic Atom Model.

Answer 21

Refer to the book.

Question 22

What are the allowed orbits in Sommerfeld’s Relativistic Atom Model? Explain something about these orbits.

Answer 22

Refer to the book. The allowed orbits are those for which the ratio of major and minor axes is that of two integers.

Question 23

Explain how, for a given value of n, n(phi) can assume only n different values, which means there can be only n elliptical orbits of different eccentricities.

Answer 23

Refer to the book for explanation.

Question 24

Explain the fine structure of H(alpha) line using Sommerfeld’s Relativistic Atom Model.

Answer 24

Refer to the book for explanation.

Question 24

Obtain the expression for the total energy of the Sommerfeld’s Relativistic Atom and compare it with that of Bohr’s. Also explain what does it mean.

Answer 24

Refer to the book.

Question 24

Explain the relativistic variation of mass and its consequences in Sommerfeld’s Relativistic Atom Model.

Answer 24

Refer to the book

Question 25

What is the fine structure constant and what is its significance?

Answer 25

Refer to the book.

Question 26

What were the drawbacks of Sommerfeld’s Relativistic Atom Model.

Answer 26

-couldn’t predict the correct numbers of fine structures of spectral lines of hydrogen.
- couldn’t explain the complex spectra of alkali metals like sodium
-Zeeman and Stark effect

Question 27

What were the main drawbacks of Bohr’s theory?

Answer 27

multiple structures of spectral lines in the simple hydrogen atom.
Zeeman and Stark effect

it couldn’t explain how the orbital electrons in an atom were distributed around the nucleus.

Question 28

Explain spatial and spin quantization according to the vector atom model.

Answer 28

Refer to the book.

Question 29

What are quantized vectors? Why are they called so?

Answer 29

Refer to the book

Question 30

Explain the quantum numbers associated with the vectors atom model.

Answer 30

Refer to the book.

Question 31

Explain the applications of Pauli Exclusion Principle.

Answer 31

…

Question 32

Derive the expression for the magnetic dipole moment due to the Orbital Motion of the Electron, and Spin motion of the electron.

Answer 32

Refer to the book for help.

Question 33

How are magnetic dipole moment for orbital motion and spin motion of the electron, in an external magnetic field calculated?

Answer 33

It is calculated for the orbital motion since the geometry is known. But for the spin motion, it is not calculated, but simply assumed, as nothing is known about the shape and charge distribution of an electron.

Question 34

What is gyromagnetic ratio?

Answer 34

ratio of magnetic dipole moment to the angular momentum

Question 35

For which results, the Stern and Gerlach Experiment’s provide evidence for?

Answer 35

It provides the direct evidence for the magnetic moments of an atom due to the orbital and spin motion of the electrons, and the space quantization of those magnetic moments.

Question 36

Sketch the diagram and explain the construction, theory and experimental results of Frank and Hertz experiment.

Answer 36

…

Question 37

What was the magnetic moment of the silver atoms used in Frank and Hertz experiments?

Answer 37

One Bohr Magneton in the direction of the field..

How though?

Question 38

What about the orbital angular momentum in Frank and Hertz experiment?

Answer 38

Fill out the answer

Question 39

What is the selection rule in case of the Sommerfeld atomic model?

Answer 39

the change in n phi should always be unity

Question 40

Write about the Larmor’s Theorem.

Answer 40

Look at the book

Question 41

What is the formula of Larmor’s angular frequency?

Answer 41

RTB

Question 42

Derive the expression for the change in KE due to the Larmor’s precession.

Answer 42

rtb

Question 43

Even though nine transitions are possible, why only three lines are seen in normal Zeeman effect?

Answer 43

rtb

Question 44

What is normal and anomalous Zeeman effect?

Answer 44

When the splitting occurs into two or three lines, the Zeeman effect is called Normal Zeeman effect, and when the splitting occurs into more than three lines, it is referred as anomalous Zeeman effect.

Question 45

Why the direction of total magnetic moment is not in alignment with the total momentum vector? Is it related to the supposition of magnetic moment due to spin motion of the electron?

Answer 45

fill out the answer