**1. What is the nature of electromagnetic radiation?**

**Answer:** Electromagnetic radiation consists of waves of electric and magnetic fields that propagate through space.

**2. Explain the photoelectric effect.**

**Answer:** The photoelectric effect is the phenomenon where electrons are emitted from a material when it is exposed to light of sufficient frequency.

**3. Describe the spectrum of the hydrogen atom.**

**Answer:** The spectrum of the hydrogen atom consists of discrete lines corresponding to transitions of electrons between energy levels, forming a series of spectral lines, including the Lyman, Balmer, and Paschen series.

**4. What are the postulates of Bohr’s model of a hydrogen atom?**

**Answer:** Bohr’s model postulates that electrons orbit the nucleus in circular paths at specific quantized energy levels, and that energy is emitted or absorbed when electrons transition between these levels.

**5. Derive the relations for the energy of the electron and radii of the different orbits in Bohr’s model.**

**Answer:** The energy of the electron in the nth orbit of a hydrogen atom is given by

and the radius of the nth orbit is given by

where m is the mass of the electron, k is Coulomb’s constant, e is the elementary charge, h is Planck’s constant, and n is the principal quantum number.

**6. What are the limitations of Bohr’s model of a hydrogen atom?**

**Answer:** Bohr’s model fails to explain the spectra of atoms with more than one electron, and it does not account for the wave nature of electrons.

**7. What is the dual nature of matter according to quantum mechanics?**

**Answer:** The dual nature of matter refers to the wave-particle duality, where particles such as electrons exhibit both wave-like and particle-like behavior.

**8. Explain de Broglie’s relationship.**

**Answer:** De Broglie’s relationship states that the wavelength (λ) of a particle is inversely proportional to its momentum

where h is Planck’s constant.

**9. What is the Heisenberg uncertainty principle?**

**Answer:** The Heisenberg uncertainty principle states that it is impossible to simultaneously determine the exact position and momentum of a particle with certainty.

**10. What are the elementary ideas of quantum mechanics?**

**Answer:** Quantum mechanics is the branch of physics that deals with the behavior of particles at the atomic and subatomic levels, incorporating wave-particle duality and probabilistic interpretations.

**11. Describe the quantum mechanical model of the atom and its important features.**

**Answer:** The quantum mechanical model describes the behavior of electrons in atoms using probability distributions rather than definite orbits, incorporating the wave nature of electrons and the quantization of energy levels.

**12. What are atomic orbitals?**

**Answer:** Atomic orbitals are regions of space around the nucleus where electrons are likely to be found, described by wave functions.

**13. Explain the variation of Ψ and Ψ ^{2} with r for 1s and 2s orbitals.**

**Answer:** For 1s and 2s orbitals, the probability density Ψ^{2} is highest at the nucleus and decreases as r increases, forming a spherical shape.

**14. What are the various quantum numbers and their significance?**

**Answer:** The principal quantum number (n) determines the energy level, the angular momentum quantum number (l) determines the shape of the orbital, and the magnetic quantum number (m_{l}) determines the orientation of the orbital in space.

**15. Describe the shapes of s, p, and d orbitals.**

**Answer:** S orbitals are spherical, p orbitals are dumbbell-shaped with two lobes, and d orbitals have more complex shapes with multiple lobes and nodes.

**16. What is electron spin and the spin quantum number?**

**Answer:** Electron spin is a fundamental property of electrons, and the spin quantum number (msm_sms) specifies the direction of spin,

**17. Explain the rules for filling electrons in orbitals, including the Aufbau principle, Pauli’s exclusion principle, and Hund’s rule.**

**Answer:** The Aufbau principle states that electrons fill orbitals starting from the lowest energy level. Pauli’s exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. Hund’s rule states that electrons occupy orbitals of the same energy singly before pairing up.

**18. What is the electronic configuration of elements?**

**Answer:** The electronic configuration of an element describes the arrangement of its electrons in various orbitals.

**19. Explain the extra stability of half-filled and completely filled orbitals.**

**Answer:** Half-filled and completely filled orbitals have extra stability due to the symmetrical distribution of electrons, which minimizes electron-electron repulsions.

**20. What is the significance of the quantum mechanical model of the atom in modern chemistry?**

**Answer:** The quantum mechanical model provides a more accurate description of atomic structure, guiding our understanding of chemical bonding, molecular geometry, and spectroscopy.