Rutherford Model and Bohr's Atom

topicmedium54 MCQ

Alpha-scattering, energy levels and hydrogen spectral series. (Physics › Atoms and Nuclei, NEET UG syllabus.)

What is Rutherford Model and Bohr's Atom?

The perpendicular distance of the initial velocity vector of the α particle from the center of the nucleus in Rutherford's scattering experiment.

Key formula / rule: Distance of Closest Approach (Rutherford)

Confusing Rutherford's model with Bohr's model limitations and successes.

Term: Impact parameter
Meaning: The perpendicular distance of the initial velocity vector of the α particle from the center of the nucleus in Rutherford's scattering experiment.

Term: Distance of closest approach
Meaning: The minimum distance to which an α particle approaches the nucleus before its kinetic energy is completely converted into electrostatic potential energy, causing it to reverse direction.

Term: Ionization energy
Meaning: The minimum energy required to remove an electron from the ground state (n=1) of an atom to an infinite distance (n=∞), making it a free electron.

Term: Excitation energy
Meaning: The energy required to move an electron from a lower energy level to a higher energy level within an atom.

Term: Spectral series
Meaning: A set of wavelengths of light emitted or absorbed by atoms as electrons transition between specific energy levels. For hydrogen, these include Lyman, Balmer, Paschen, Brackett, and Pfund series.

Describe Rutherford's α-scattering experiment and its conclusions.
Explain the limitations of Rutherford's atomic model.
State Bohr's postulates for the hydrogen atom.
Derive expressions for Bohr's radius, velocity, and energy of an electron.
Calculate energy levels and wavelengths of spectral lines for hydrogen and hydrogen-like atoms.
Identify the different spectral series of hydrogen (Lyman, Balmer, Paschen, Brackett, Pfund) and their regions of the electromagnetic spectrum.

Name: Distance of Closest Approach (Rutherford)
Note: K is the initial kinetic energy of the α particle, Z is the atomic number of the target nucleus.
Expression: r₀ = (1 / (4πε₀)) * (2Ze²) / K

Name: Bohr's Quantization Condition
Note: n is the principal quantum number (1, 2, 3...), ħ is reduced Planck's constant.
Expression: L = mvr = nħ = n(h/2π)

Name: Bohr's Radius
Note: r_n is the radius of the nth orbit, m is electron mass, e is electron charge, ε₀ is permittivity of free space.
Expression: r_n = (n²h²ε₀) / (πme²Z) = 0.529 * (n²/Z) Å

Name: Bohr's Energy
Note: E_n is the energy of the electron in the nth orbit. Negative sign indicates the electron is bound to the nucleus.
Expression: E_n = - (me⁴Z²) / (8ε₀²h²n²) = -13.6 * (Z²/n²) eV

Name: Energy of Emitted/Absorbed Photon
Note: E₁ and E₂ are initial and final energy levels, h is Planck's constant, ν is frequency, c is speed of light, λ is wavelength.
Expression: ΔE = E₂ - E₁ = hν = hc/λ

Name: Rydberg Formula for Wavelength
Note: R is Rydberg constant (1.097 × 10⁷ m⁻¹), n₁ is the lower energy level, n₂ is the higher energy level (n₂ > n₁).
Expression: 1/λ = RZ² * (1/n₁² - 1/n₂²)

According to Bohr's model, the angular momentum of an electron in a stationary orbit is an integral multiple of:…
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The radius of the first Bohr orbit for a hydrogen atom is approximately 0.53 Angstrom. What is the radius of the third Bohr orbit for the hydrogen atom?…
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Calculate the energy required to excite an electron from the ground state (n=1) to the first excited state (n=2) in a hydrogen atom. (Given: Ground state energy of hydrogen atom = -13.6 eV)…
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