Structure of Atom Class 11 Notes

• Electron — charge −1.6 × 10⁻¹⁹ C, mass ≈ 9.1 × 10⁻³¹ kg (discovered by Thomson).
• Proton — charge +1.6 × 10⁻¹⁹ C, mass ≈ 1.67 × 10⁻²⁷ kg (Rutherford).
• Neutron — no charge, mass slightly more than the proton (Chadwick).

• Electrons move in fixed, allowed circular orbits (shells n = 1, 2, 3...) where angular momentum is quantised.
• Energy is absorbed or emitted only when an electron jumps between orbits — as photons with exact energy.
• Works beautifully for hydrogen (one electron) but fails for multi-electron atoms.

• Aufbau principle — electrons fill orbitals in order of increasing energy: 1s < 2s < 2p < 3s < 3p < 4s < 3d...
• Pauli exclusion principle — no two electrons in an atom can have all four quantum numbers identical, so each orbital holds at most two electrons with opposite spins.
• Hund's rule — within a subshell, electrons first occupy each orbital singly with parallel spins before pairing.

Example: Write the electronic configuration of ${}_{26}\text{Fe}$ (Z = 26) and state its total unpaired electrons.

Solution: Configuration is $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^6$. By Hund's rule the 3d⁶ subshell has 4 unpaired — filling the five d-orbitals singly first gives four unpaired electrons and one pair.

Example: What is the de Broglie wavelength of an electron moving at $2\times 10^6\text{m/s}$? (h = 6.626 × 10⁻³⁴ J·s, mₑ = 9.1 × 10⁻³¹ kg)

Solution: $\lambda =\frac{6.626\times 10^{-34}}{9.1\times 10^{-31}\times 2\times 10^6}\approx 3.64\times 10^{-10}\text{m}$ (≈ 3.6 Å, in the same range as atomic sizes).

Exercises (NCERT Q2.1–Q2.67)

• 2.1) (i) Calculate the number of electrons which will together weigh one gram. (ii) Calculate the mass and charge of one mole of electrons.
• 2.2) (i) Calculate the total number of electrons present in one mole of methane. (ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of ¹⁴C (assume mass of a neutron = 1.675 × 10⁻²⁷ kg). (iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH₃ at STP. Will the answer change if the temperature and pressure are changed?
• 2.3) How many neutrons and protons are there in the following nuclei? ₆¹³C, ₈¹⁶O, ₁₂²⁴Mg, ₂₆⁵⁶Fe, ₃₈⁸⁸Sr.
• 2.4) Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A): (i) Z = 17, A = 35 (ii) Z = 92, A = 233 (iii) Z = 4, A = 9.
• 2.5) Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber (ν̄) of the yellow light.
• 2.6) Find the energy of each of the photons which (i) correspond to light of frequency 3 × 10¹⁵ Hz (ii) have a wavelength of 0.50 Å.
• 2.7) Calculate the wavelength, frequency and wavenumber of a light wave whose period is 2.0 × 10⁻¹⁰ s.
• 2.8) What is the number of photons of light with a wavelength of 4000 pm that provide 1 J of energy?
• 2.9) A photon of wavelength 4 × 10⁻⁷ m strikes a metal surface, the work function of the metal being 2.13 eV. Calculate (i) the energy of the photon (in eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron. (1 eV = 1.6020 × 10⁻¹⁹ J.)
• 2.10) Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol⁻¹.
• 2.11) A 25 watt bulb emits monochromatic yellow light of wavelength 0.57 µm. Calculate the rate of emission of quanta per second.
• 2.12) Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength 6800 Å. Calculate the threshold frequency (ν₀) and work function (W₀) of the metal.
• 2.13) What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2?
• 2.14) How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of the H atom (energy required to remove the electron from n = 1 orbit).
• 2.15) What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to the ground state?
• 2.16) (i) The energy associated with the first orbit in the hydrogen atom is −2.18 × 10⁻¹⁸ J atom⁻¹. What is the energy associated with the fifth orbit? (ii) Calculate the radius of Bohr's fifth orbit for the hydrogen atom.
• 2.17) Calculate the wavenumber for the longest wavelength transition in the Balmer series of atomic hydrogen.
• 2.18) What is the energy in joules required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is −2.18 × 10⁻¹¹ ergs.
• 2.19) The electron energy in the hydrogen atom is given by E_n = (−2.18 × 10⁻¹⁸)/n² J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?
• 2.20) Calculate the wavelength of an electron moving with a velocity of 2.05 × 10⁷ m s⁻¹.
• 2.21) The mass of an electron is 9.1 × 10⁻³¹ kg. If its K.E. is 3.0 × 10⁻²⁵ J, calculate its wavelength.
• 2.22) Which of the following are isoelectronic species, i.e. those having the same number of electrons? Na⁺, K⁺, Mg²⁺, Ca²⁺, S²⁻, Ar.
• 2.23) (i) Write the electronic configurations of the following ions: (a) H⁻ (b) Na⁺ (c) O²⁻ (d) F⁻. (ii) What are the atomic numbers of elements whose outermost electrons are represented by (a) 3s¹ (b) 2p³ (c) 3p⁵? (iii) Which atoms are indicated by the following configurations? (a) [He]2s¹ (b) [Ne]3s²3p³ (c) [Ar]4s²3d¹.
• 2.24) What is the lowest value of n that allows g orbitals to exist?
• 2.25) An electron is in one of the 3d orbitals. Give the possible values of n, l and m_l for this electron.
• 2.26) An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the electronic configuration of the element.
• 2.27) Give the number of electrons in the species H₂⁺, H₂ and O₂⁺.
• 2.28) (i) An atomic orbital has n = 3. What are the possible values of l and m_l? (ii) List the quantum numbers (m_l and l) of electrons for the 3d orbital. (iii) Which of the following orbitals are possible? 1p, 2s, 2p and 3f.
• 2.29) Using s, p, d notations, describe the orbital with the following quantum numbers. (a) n = 1, l = 0 (b) n = 3, l = 1 (c) n = 4, l = 2 (d) n = 4, l = 3.
• 2.30) Explain, giving reasons, which of the following sets of quantum numbers are not possible. (a) n = 0, l = 0, m_l = 0, m_s = +1/2 (b) n = 1, l = 0, m_l = 0, m_s = −1/2 (c) n = 1, l = 1, m_l = 0, m_s = +1/2 (d) n = 2, l = 1, m_l = 0, m_s = −1/2 (e) n = 3, l = 3, m_l = −3, m_s = +1/2 (f) n = 3, l = 1, m_l = 0, m_s = +1/2.
• 2.31) How many electrons in an atom may have the following quantum numbers? (a) n = 4, m_s = −1/2 (b) n = 3, l = 0.
• 2.32) Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.
• 2.33) What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of the He⁺ spectrum?
• 2.34) Calculate the energy required for the process He⁺(g) → He²⁺(g) + e⁻. The ionisation energy for the H atom in the ground state is 2.18 × 10⁻¹⁸ J atom⁻¹.
• 2.35) If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be placed side by side in a straight line across a length of a scale of 20 cm.
• 2.36) 2 × 10⁸ atoms of carbon are arranged side by side. Calculate the radius of the carbon atom if the length of this arrangement is 2.4 cm.
• 2.37) The diameter of a zinc atom is 2.6 Å. Calculate (a) the radius of a zinc atom in pm and (b) the number of atoms present in a length of 1.6 cm if the zinc atoms are arranged side by side lengthwise.
• 2.38) A certain particle carries 2.5 × 10⁻¹⁶ C of static electric charge. Calculate the number of electrons present in it.
• 2.39) In Millikan's experiment, the static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is −1.282 × 10⁻¹⁸ C, calculate the number of electrons present on it.
• 2.40) In Rutherford's experiment, generally a thin foil of heavy atoms, like gold, platinum etc., is used to be bombarded by the α-particles. If the thin foil of light atoms like aluminium etc. is used, what difference would be observed from the above results?
• 2.41) Symbols ³⁵⁷⁹Br and ⁷⁹Br can be written, whereas symbols ₇₉³⁵Br and ³⁵Br are not acceptable. Answer briefly.
• 2.42) An element with mass number 81 contains 31.7% more neutrons as compared to protons. Assign the atomic symbol.
• 2.43) An ion with mass number 37 possesses one unit of negative charge. If the ion contains 11.1% more neutrons than the electrons, find the symbol of the ion.
• 2.44) An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than electrons. Assign the symbol to this ion.
• 2.45) Arrange the following types of radiations in increasing order of frequency: (a) radiation from a microwave oven (b) amber light from a traffic signal (c) radiation from FM radio (d) cosmic rays from outer space and (e) X-rays.
• 2.46) A nitrogen laser produces radiation at a wavelength of 337.1 nm. If the number of photons emitted is 5.6 × 10²⁴, calculate the power of this laser.
• 2.47) Neon gas is generally used in sign boards. If it emits strongly at 616 nm, calculate (a) the frequency of emission, (b) the distance travelled by this radiation in 30 s, (c) the energy of a quantum, and (d) the number of quanta present if it produces 2 J of energy.
• 2.48) In astronomical observations, signals observed from distant stars are generally weak. If the photon detector receives a total of 3.15 × 10⁻¹⁸ J from the radiations of 600 nm, calculate the number of photons received by the detector.
• 2.49) Lifetimes of molecules in excited states are often measured by using a pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse is 2.5 × 10¹⁵, calculate the energy of the source.
• 2.50) The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and the energy difference between the two excited states.
• 2.51) The work function for a caesium atom is 1.9 eV. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength of 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.
• 2.52) Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) the threshold wavelength and (b) Planck's constant. λ (nm): 500, 450, 400. v × 10⁻⁵ (cm s⁻¹): 2.55, 4.35, 5.35.
• 2.53) The ejection of a photoelectron from silver metal in the photoelectric effect experiment can be stopped by applying a voltage of 0.35 V when radiation of 256.7 nm is used. Calculate the work function of silver metal.
• 2.54) If a photon of wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 10⁷ m s⁻¹, calculate the energy with which it is bound to the nucleus.
• 2.55) Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as ν = 3.29 × 10¹⁵ (Hz)(1/3² − 1/n²). Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.
• 2.56) Calculate the wavelength for the emission transition if it starts from the orbit having radius 1.3225 nm and ends at 211.6 pm. Name the series to which this transition belongs and the region of the spectrum.
• 2.57) Dual behaviour of matter proposed by de Broglie led to the discovery of the electron microscope, often used for highly magnified images of biological molecules and other types of material. If the velocity of the electron in this microscope is 1.6 × 10⁶ m s⁻¹, calculate the de Broglie wavelength associated with this electron.
• 2.58) Similar to electron diffraction, a neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.
• 2.59) If the velocity of the electron in Bohr's first orbit is 2.19 × 10⁶ m s⁻¹, calculate the de Broglie wavelength associated with it.
• 2.60) The velocity associated with a proton moving in a potential difference of 1000 V is 4.37 × 10⁵ m s⁻¹. If a hockey ball of mass 0.1 kg is moving with this velocity, calculate the wavelength associated with this velocity.
• 2.61) If the position of the electron is measured within an accuracy of ±0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is h/(4π × 0.05 nm), is there any problem in defining this value?
• 2.62) The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combinations has/have the same energy, list them. (1) n = 4, l = 2, m_l = −2, m_s = −1/2 (2) n = 3, l = 2, m_l = 1, m_s = +1/2 (3) n = 4, l = 1, m_l = 0, m_s = +1/2 (4) n = 3, l = 2, m_l = −2, m_s = −1/2 (5) n = 3, l = 1, m_l = −1, m_s = +1/2 (6) n = 4, l = 1, m_l = 0, m_s = +1/2.
• 2.63) The bromine atom possesses 35 electrons. It contains 6 electrons in the 2p orbital, 6 electrons in the 3p orbital and 5 electrons in the 4p orbital. Which of these electrons experiences the lowest effective nuclear charge?
• 2.64) Among the following pairs of orbitals, which orbital will experience the larger effective nuclear charge? (i) 2s and 3s (ii) 4d and 4f (iii) 3d and 3p.
• 2.65) The unpaired electrons in Al and Si are present in the 3p orbital. Which electrons will experience more effective nuclear charge from the nucleus?
• 2.66) Indicate the number of unpaired electrons in: (a) P (b) Si (c) Cr (d) Fe (e) Kr.
• 2.67) (a) How many subshells are associated with n = 4? (b) How many electrons will be present in the subshells having an m_s value of −1/2 for n = 4?

Answers at a glance

1. 1
   Q2.1 → (i) 1.098 × 10²⁷ electrons (ii) mass = 5.48 × 10⁻⁷ kg; charge = 9.65 × 10⁴ C.
2. 2
   Q2.2 → (i) 6.023 × 10²⁴ electrons. (ii) 2.4088 × 10²¹ neutrons; 4.035 × 10⁻⁶ kg. (iii) 1.2044 × 10²² protons; 2.0138 × 10⁻⁵ kg. Answers are unchanged by temperature and pressure.
3. 3
   Q2.3 → C: 6 p, 7 n; O: 8 p, 8 n; Mg: 12 p, 12 n; Fe: 26 p, 30 n; Sr: 38 p, 50 n.
4. 4
   Q2.4 → (i) ₁₇³⁵Cl (ii) ₉₂²³³U (iii) ₄⁹Be.
5. 5
   Q2.5 → Frequency = 5.17 × 10¹⁴ s⁻¹; wavenumber = 1.72 × 10⁶ m⁻¹.
6. 6
   Q2.6 → (i) 1.99 × 10⁻¹⁸ J (ii) 3.98 × 10⁻¹⁵ J.
7. 7
   Q2.7 → Frequency = 5 × 10⁹ s⁻¹; wavelength = 6.0 × 10⁻² m; wavenumber = 16.66 m⁻¹.
8. 8
   Q2.8 → 2.012 × 10¹⁶ photons.
9. 9
   Q2.9 → (i) 3.10 eV (ii) 0.97 eV (iii) v = 5.84 × 10⁵ m s⁻¹.
10. 10
    Q2.10 → 494 kJ mol⁻¹.
11. 11
    Q2.11 → 7.17 × 10¹⁹ quanta per second.
12. 12
    Q2.12 → Threshold frequency = 4.41 × 10¹⁴ s⁻¹; work function = 2.92 × 10⁻¹⁹ J.
13. 13
    Q2.13 → 486 nm (emitted light of the Balmer series).
14. 14
    Q2.14 → 8.72 × 10⁻²⁰ J (from n = 5) versus 2.18 × 10⁻¹⁸ J (from n = 1); ionising from n = 5 needs only 1/25 of the ground-state ionisation enthalpy.
15. 15
    Q2.15 → 15 emission lines.
16. 16
    Q2.16 → (i) −8.72 × 10⁻²⁰ J (ii) r₅ = 1.3225 nm.
17. 17
    Q2.17 → 1.52 × 10⁶ m⁻¹ (the H-alpha line, 656 nm).
18. 18
    Q2.18 → Energy required = 2.09 × 10⁻¹⁸ J; wavelength of the emitted light = 9.5 × 10⁻⁸ m = 95 nm.
19. 19
    Q2.19 → Energy required = 5.45 × 10⁻¹⁹ J; longest wavelength = 3.65 × 10⁻⁵ cm (364.7 nm).
20. 20
    Q2.20 → 3.55 × 10⁻¹¹ m (about 35.5 pm).
21. 21
    Q2.21 → 8.96 × 10⁻⁷ m ≈ 896 nm.
22. 22
    Q2.22 → Na⁺ and Mg²⁺ are isoelectronic (10 electrons); K⁺, Ca²⁺, S²⁻ and Ar are isoelectronic (18 electrons).
23. 23
    Q2.23 → (i) H⁻ = 1s²; Na⁺ = 1s²2s²2p⁶; O²⁻ = 1s²2s²2p⁶; F⁻ = 1s²2s²2p⁶. (ii) 11, 7, 17. (iii) Li, P, Sc.
24. 24
    Q2.24 → n = 5.
25. 25
    Q2.25 → n = 3, l = 2, m_l = −2, −1, 0, 1, 2.
26. 26
    Q2.26 → (i) 29 protons (copper, Z = 29). (ii) 1s²2s²2p⁶3s²3p⁶3d¹⁰4s¹ (special stability of the fully filled 3d subshell).
27. 27
    Q2.27 → H₂⁺ = 1, H₂ = 2, O₂⁺ = 15 electrons.
28. 28
    Q2.28 → (i) l = 0, 1, 2 with m_l as listed. (ii) l = 2, m_l = −2, −1, 0, 1, 2. (iii) Only 2s and 2p are possible; 1p and 3f are not.
29. 29
    Q2.29 → (a) 1s (b) 3p (c) 4d (d) 4f.
30. 30
    Q2.30 → Not possible: (a) n = 0, (c) l = 1 for n = 1, (e) l = 3 for n = 3. Possible: (b), (d), (f).
31. 31
    Q2.31 → (a) 16 electrons (b) 2 electrons.
32. 32
    Q2.32 → Proved: 2πr = nλ — the orbital circumference is an integral multiple of the electron's de Broglie wavelength.
33. 33
    Q2.33 → The n = 2 to n = 1 transition of hydrogen has the same wavelength as the n = 4 → n = 2 transition of He⁺ (ν̄ = 3R/4).
34. 34
    Q2.34 → 8.72 × 10⁻¹⁸ J (four times the hydrogen ionisation energy, since Z² = 4).
35. 35
    Q2.35 → 1.33 × 10⁹ atoms.
36. 36
    Q2.36 → Radius = 6.0 × 10⁻¹¹ m (0.6 Å).
37. 37
    Q2.37 → (a) 130 pm (b) 6.15 × 10⁷ atoms.
38. 38
    Q2.38 → 1560 electrons.
39. 39
    Q2.39 → 8 electrons.
40. 40
    Q2.40 → Light-atom foil — few α-particles are deflected and large-angle scattering is drastically reduced, because the small nuclear charge exerts little repulsion.
41. 41
    Q2.41 → Z is fixed for an element but A changes with isotope; the subscript/superscript convention AZX allows ₃₅⁷⁹Br and ⁷⁹Br but rejects ₇₉³⁵Br and ³⁵Br.
42. 42
    Q2.42 → ₃₅⁸¹Br.
43. 43
    Q2.43 → ₃₇¹⁷Cl⁻ (the chloride-37 ion).
44. 44
    Q2.44 → ₅₆²⁶Fe³⁺.
45. 45
    Q2.45 → Increasing frequency: FM radio < microwave oven < amber light < X-rays < cosmic rays.
46. 46
    Q2.46 → Power = 3.33 × 10⁶ J (equivalent to 3.33 × 10⁶ W for this energy emitted per second).
47. 47
    Q2.47 → (a) 4.87 × 10¹⁴ s⁻¹ (b) 9.0 × 10⁹ m (c) 3.23 × 10⁻¹⁹ J (d) 6.2 × 10¹⁸ quanta.
48. 48
    Q2.48 → About 9.5 (≈ 10) photons.
49. 49
    Q2.49 → 8.28 × 10⁻¹⁰ J.
50. 50
    Q2.50 → ν₁ = 5.093 × 10¹⁴ s⁻¹; ν₂ = 5.088 × 10¹⁴ s⁻¹; ΔE = 3.31 × 10⁻²² J.
51. 51
    Q2.51 → (a) λ₀ = 653 nm (b) ν₀ = 4.593 × 10¹⁴ s⁻¹ (c) KE = 9.31 × 10⁻²⁰ J; v = 4.52 × 10⁵ m s⁻¹.
52. 52
    Q2.52 → (a) λ₀ ≈ 540 nm. (b) Not computable — the supplied velocities are mutually inconsistent and do not yield Planck's constant.
53. 53
    Q2.53 → Work function of silver = 4.48 eV.
54. 54
    Q2.54 → Binding energy ≈ 7.6 × 10³ eV (12.2 × 10⁻¹⁶ J).
55. 55
    Q2.55 → n = 5; the transition lies in the infra-red region.
56. 56
    Q2.56 → Transition is 5 → 2; Balmer series; λ = 434 nm in the visible region.
57. 57
    Q2.57 → 455 pm.
58. 58
    Q2.58 → v = 494 m s⁻¹.
59. 59
    Q2.59 → 332 pm.
60. 60
    Q2.60 → 1.52 × 10⁻³⁸ m.
61. 61
    Q2.61 → Δp = 2.637 × 10⁻²³ kg m s⁻¹. The stated momentum 1.06 × 10⁻²⁴ kg m s⁻¹ is smaller than the uncertainty, so the value cannot be defined.
62. 62
    Q2.62 → 5 (3p) < 2 = 4 (3d) < 3 = 6 (4p) < 1 (4d). Pairs (2,4) and (3,6) have equal energies.
63. 63
    Q2.63 → The 5 electrons in the 4p orbital experience the lowest effective nuclear charge (being farthest from the nucleus and most heavily shielded).
64. 64
    Q2.64 → (i) 2s (ii) 4d (iii) 3p.
65. 65
    Q2.65 → The 3p electrons of silicon (Si, Z = 14) experience a greater effective nuclear charge than those of aluminium (Al, Z = 13).
66. 66
    Q2.66 → (a) P = 3 (b) Si = 2 (c) Cr = 6 (d) Fe = 4 (e) Kr = 0.
67. 67
    Q2.67 → (a) 4 subshells (4s, 4p, 4d, 4f) (b) 16 electrons.

MCQ Questions

1 Mark Questions

1. 1
   What is an isotope? (Ans: atoms of the same element with the same atomic number but different mass numbers)
2. 2
   State de Broglie's relation. (Ans: λ = h/mv — every moving particle has an associated wavelength)
3. 3
   Write the value of the Rydberg constant for hydrogen. (Ans: R_H ≈ 1.097 × 10⁷ m⁻¹)
4. 4
   State the Heisenberg uncertainty principle. (Ans: it is impossible to determine simultaneously the exact position and momentum of an electron; Δx × Δp ≥ h/4π)

2 Mark Questions

1. 1
   What are the differences between the Thomson and Rutherford models of the atom? (Ans: plum-pudding uniform positive charge vs tiny dense positive nucleus with mostly empty space)
2. 2
   Calculate the de Broglie wavelength of an electron travelling at 6.0 × 10⁴ m s⁻¹ (mₑ = 9.1 × 10⁻³¹ kg). (Ans: λ ≈ 1.2 × 10⁻⁸ m = 12 nm)
3. 3
   Explain how the Pauli exclusion principle limits the number of electrons in an orbital. (Ans: max two electrons per orbital with opposite spins — no two electrons can have all four quantum numbers the same)

3 Mark Questions

1. 1
   Describe Bohr's model of the hydrogen atom, giving the expressions for the radius and energy of the nth orbit. (Ans: rₙ = 0.529(n²/Z) Å; Eₙ = −13.6(Z²/n²) eV)
2. 2
   State the Aufbau principle, Hund's rule and the Pauli exclusion principle, and write the ground-state configuration of chromium (Z = 24). (Ans: [Ar] 3d⁵ 4s¹)
3. 3
   Explain the shapes of s, p and d orbitals. (Ans: s — spherical; p — dumbbell along the three axes (pₓ, pᵧ, p₂); d — four-leaf clover shapes, five orientations including dₓ²₋ᵧ² and d₂²)

5 Mark Questions

1. 1
   What is the photoelectric effect? Explain how Einstein's theory explains it and calculate the energy of a photon of wavelength 500 nm (h = 6.626 × 10⁻³⁴ J s). (Ans: E = hc/λ ≈ 3.98 × 10⁻¹⁹ J; one photon releases one electron above the threshold frequency)
2. 2
   Write the complete set of quantum numbers (n, l, m, s) describing the 3d electrons of an atom, explain the significance of each quantum number, and derive the Rydberg formula for the hydrogen spectrum using Bohr's energy expression.