Rutherford’s Model of Atom
• Rutherford’s Experiment (1911):
o Geiger and Marsden bombarded gold foil with α-particles.
o Observations:
1. Most α-particles passed through the foil
undeflected.
2. A small number (1 in 8000) suffered large
angle deflections, some even retraced
their path.
o Conclusion:
1. The atom is mostly empty space.
2. The positive charge and almost all the mass are concentrated in a tiny, dense
region at the center called the nucleus.
3. The negatively charged electrons are outside the nucleus.
4. Coulomb’s law holds at atomic distances.
• Impact Parameter:
o The perpendicular distance of the initial velocity vector of α-particle from the nucleus.
o For a head-on approach, the impact parameter is 0.
• Distance of Closest Approach:
o Smallest distance of approach of an α-particle to the nucleus gives the size of the
nucleus.
Bohr Model of Atom
• Bohr's Modifications to Rutherford's Model:
o Bohr introduced a quantum aspect to Rutherford's model to explain the
hydrogen spectrum and the stability of atoms.
• Postulates of Bohr's Theory:
1.Stationary Orbits: Electrons revolve around the nucleus in stable, fixed orbits with no
radiation emission.
2.Quantum Condition: The angular momentum of an electron in these orbits is
quantized and given by:
𝑚𝑣𝑟 = 𝑛ℏ(𝑛 = 1,2,3, … )
where 𝑚 is the electron mass, 𝑣 is the velocity, 𝑟 is the radius of the orbit, and ℏ is the
reduced Planck's constant.
3.Energy Transitions: An electron can absorb or emit energy when jumping from one
orbit to another. The energy of emitted/absorbed photon is related to the energy
difference between the orbits:
𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = 𝐸𝑖 − 𝐸𝑓 = ℎ𝜈
where 𝐸𝑖 and 𝐸𝑓 are the energies of the initial and final states, and 𝜈 is the frequency of
the photon.
• Radius of Electron Orbits: The radius of the nth orbit of an electron in a hydrogen atom
is given by:
where 𝑛 is the principal quantum number, me is the electron mass, 𝑒 is the electron
charge, and 𝑍 is the atomic number.
• Energy of Electrons in Orbits: The energy of the electron in the nth orbit is:
For hydrogen (Z=1Z = 1Z=1):
Hydrogen Line Spectrum
• Energy Levels of Hydrogen Atom:
o The energy of the electron in the hydrogen atom is quantized and depends on
the principal quantum number 𝑛.
o For the hydrogen atom, the energy levels are given by:
• Hydrogen Emission Spectrum:
o Consists of discrete lines corresponding to transitions between different energy
levels.
o Series of Lines:
1. Lyman Series: Transitions to 𝑛 = 1𝑛 = 1𝑛 = 1, in the ultraviolet region.
2. Balmer Series: Transitions to 𝑛 = 2𝑛 = 2𝑛 = 2, in the visible region.
3. Paschen Series: Transitions to 𝑛 = 3𝑛 = 3𝑛 = 3, in the infrared region.
4. Brackett Series: Transitions to 𝑛 = 4𝑛 = 4𝑛 = 4, in the infrared region.
5. Pfund Series: Transitions to 𝑛 = 5𝑛 = 5𝑛 = 5, in the infrared region.
• Hydrogen Absorption Spectrum:
o Contains only the Lyman series (from higher to 𝑛 = 1𝑛 = 1𝑛 = 1).
• Explanation of Hydrogen Spectrum:
o The wavelength of emitted light is related to the energy difference between the
initial and final states, given by:
where 𝑛𝑓 and 𝑛𝑖 are the final and initial quantum numbers, and 𝑅𝐻 is the
Rydberg constant.
o The wave number (reciprocal of wavelength) for emitted radiation is given by:
