CSIR NET Physical Sciences Atomic & Molecular Physics Syllabus

Atomic & Molecular Physics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Atomic & Molecular Physics in CSIR NET Physical Sciences, not a summary of it.

1. 1

   Quantum states of an electron in an atom

   1 topic

   • Electron spin
2. 2

   Spectrum of helium and alkali atom

   1 topic

   • Relativistic corrections for energy levels of hydrogen atom
     • Hyperfine structure and isotopic shift
     • Width of spectrum lines
3. 3

   LS & JJ couplings

   overview

   Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

4. 4

   Zeeman effect

   overview

   Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

5. 5

   Paschen-Bach effect

   overview

   Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

6. 6

   Stark effect

   overview

   Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

7. 7

   Electron spin resonance

   overview

   Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

8. 8

   Nuclear magnetic resonance

   1 topic

   • Chemical shift
9. 9

   Frank-Condon principle

   overview

   Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

10. 10

    Born-Oppenheimer approximation

    overview

    Examined as a single unit within Atomic & Molecular Physics — no further topic split in the official outline.

11. 11

    Electronic, rotational, vibrational and Raman spectra of diatomic molecules

    1 topic

    • Selection rules
12. 12

    Lasers

    7 topics

    • Spontaneous and stimulated emission
    • Einstein A & B coefficients
    • Optical pumping
    • Population inversion
    • Rate equation
    • Modes of resonators
    • Coherence length

Atomic & Molecular Physics flashcards for CSIR NET Physical Sciences

23 of 51 cards from the Atomic & Molecular Physics deck — real questions with worked answers.

1. What is electron spin, and what is the value of the electron's spin quantum number $s$?

   Electron spin is an intrinsic angular momentum of the electron with no classical analogue. The spin quantum number is $s = \frac{1}{2}$, so the spin magnetic quantum number takes values $m_s = \pm\frac{1}{2}$.

2. Write the magnitude of the electron's spin angular momentum vector $\vec{S}$.

   $$|\vec{S}| = \sqrt{s(s+1)}\,\hbar = \sqrt{\tfrac{1}{2}\left(\tfrac{1}{2}+1\right)}\,\hbar = \frac{\sqrt{3}}{2}\,\hbar$$

3. What is the spin magnetic moment of the electron and the value of the electron spin g-factor?

   $$\vec{\mu}_s = -g_s\,\frac{\mu_B}{\hbar}\,\vec{S},\qquad g_s \approx 2.0023$$ where $\mu_B = \dfrac{e\hbar}{2m_e}$ is the Bohr magneton.

4. Name the three relativistic corrections that produce the fine structure of the hydrogen atom.

   (1) The relativistic kinetic-energy correction (mass–velocity term), (2) the spin–orbit coupling, and (3) the Darwin term.

5. Give the total fine-structure energy correction for hydrogen and state on which quantum numbers it depends.

   $$\Delta E_{fs} = -\frac{E_n\,\alpha^{2}}{n^{2}}\left(\frac{n}{j+\tfrac{1}{2}} - \frac{3}{4}\right)$$ It depends only on $n$ and $j$ (not on $l$ separately), where $\alpha$ is the fine-structure constant.

6. Write the mass–velocity (relativistic kinetic energy) correction term in the hydrogen Hamiltonian.

   $$H_{rel} = -\frac{\hat{p}^{4}}{8 m_e^{3} c^{2}}$$ It arises from expanding the relativistic kinetic energy $\sqrt{p^{2}c^{2}+m^{2}c^{4}}$.

7. Write the spin–orbit interaction Hamiltonian for the hydrogen atom.

   $$H_{SO} = \frac{1}{2 m_e^{2} c^{2}}\,\frac{1}{r}\frac{dV}{dr}\,\vec{L}\cdot\vec{S}$$ It couples the electron's orbital and spin angular momenta.

8. In terms of $j$, $l$ and $s$, evaluate $\vec{L}\cdot\vec{S}$ used in spin–orbit coupling.

   $$\vec{L}\cdot\vec{S} = \frac{1}{2}\left[\,j(j+1) - l(l+1) - s(s+1)\,\right]\hbar^{2}$$

9. What is the Darwin term and which states does it affect?

   The Darwin term, $H_D = \dfrac{\pi \hbar^{2}}{2 m_e^{2} c^{2}}\,\dfrac{Ze^{2}}{4\pi\varepsilon_0}\,\delta^{3}(\vec{r})$, arises from the electron's Zitterbewegung. Because it depends on $|\psi(0)|^{2}$, it affects only $s$ states ($l=0$).

10. What is the order of magnitude of the fine-structure splitting relative to the Bohr energy levels?

    The fine structure is smaller than the gross (Bohr) structure by a factor of order $\alpha^{2} \approx (1/137)^{2} \approx 5\times10^{-5}$.

11. What is the origin of hyperfine structure in atomic spectra?

    Hyperfine structure arises from the interaction between the nuclear magnetic moment (and electric quadrupole moment) and the magnetic field/electric field gradient produced by the electrons, i.e. coupling of nuclear spin $\vec{I}$ with electronic angular momentum $\vec{J}$.

12. Define the total atomic angular momentum $\vec{F}$ in hyperfine structure and give the allowed values of $F$.

    $$\vec{F} = \vec{I} + \vec{J},\qquad F = |I-J|,\,|I-J|+1,\dots,\,I+J$$ where $\vec{I}$ is nuclear spin and $\vec{J}$ is total electronic angular momentum.

13. Write the magnetic dipole hyperfine interaction energy and the corresponding interval rule.

    $$E_{hf} = \frac{A}{2}\left[F(F+1) - I(I+1) - J(J+1)\right]$$ Interval rule: the splitting between adjacent levels $F$ and $F-1$ is $\Delta E = A\,F$, proportional to $F$.

14. By roughly what factor is hyperfine structure smaller than fine structure?

    By about the ratio of electron to nucleon mass, $m_e/m_p \approx 1/1836$, since the nuclear magneton $\mu_N = \dfrac{e\hbar}{2m_p}$ is about $1836$ times smaller than the Bohr magneton.

15. What is the isotope shift, and what are its two principal contributions?

    The isotope shift is the small difference in spectral line frequencies between different isotopes of an element. Its two contributions are the mass shift (normal + specific mass shift, from finite nuclear mass / reduced mass) and the volume (field) shift (from finite nuclear size and charge distribution).

16. Distinguish the normal mass shift from the specific mass shift in isotope shifts.

    The normal mass shift comes from the change in reduced mass $\mu = \dfrac{m_e M}{m_e + M}$ for a single electron and scales as $\propto \dfrac{m_e}{M}$. The specific (mass) shift arises from electron–electron momentum correlation in many-electron atoms and has no simple sign.

17. For which atoms does the mass (isotope) shift dominate, and for which does the volume shift dominate?

    The mass shift dominates for light atoms (small $Z$), while the volume/field shift dominates for heavy atoms (large $Z$), where the nuclear charge volume is larger and inner electrons probe the nucleus more strongly.

18. List the main mechanisms that contribute to the width of spectral lines.

    (1) Natural (lifetime) broadening, (2) Doppler broadening (thermal motion), (3) Collision/pressure broadening, and (4) instrumental broadening.

19. State the natural line width in terms of excited-state lifetime, and the resulting line shape.

    $$\Delta\nu_{nat} = \frac{1}{2\pi\tau}$$ where $\tau$ is the lifetime of the excited state. The natural line shape is a Lorentzian, and it follows from the energy–time uncertainty $\Delta E\,\Delta t \approx \hbar$.

20. Write the Doppler line width (FWHM) of a spectral line at temperature $T$.

    $$\Delta\nu_D = \nu_0\,\sqrt{\frac{8 k_B T \ln 2}{M c^{2}}}$$ The Doppler-broadened profile is Gaussian; $M$ is the atomic mass.

21. Classify natural, Doppler, and collision broadening as homogeneous or inhomogeneous, and give their line shapes.

    Natural broadening: homogeneous, Lorentzian. Collision (pressure) broadening: homogeneous, Lorentzian. Doppler broadening: inhomogeneous, Gaussian. (A convolution of Gaussian and Lorentzian gives a Voigt profile.)

22. What is the chemical shift in NMR spectroscopy, and why does it occur?

    The chemical shift is the small change in the resonance frequency of a nucleus due to shielding of the external magnetic field by surrounding electrons. The effective field is $B_{eff} = B_0(1-\sigma)$, where $\sigma$ is the shielding constant, so chemically inequivalent nuclei resonate at different frequencies.

23. Write the definition of the NMR chemical shift $\delta$ in ppm.

    $$\delta = \frac{\nu_{sample} - \nu_{ref}}{\nu_{ref}}\times 10^{6}\ \text{(ppm)}$$ usually referenced to tetramethylsilane (TMS) for $^{1}\text{H}$ and $^{13}\text{C}$.

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