Structure of the Atom

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1. The entire positive charge and most of the mass is concentrated in a very small central region called nucleus (~10⁻¹⁵ m) 2. Negatively charged electrons revolve around the nucleus at a distance 3.

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1. Most α-particles passed straight through with little or no deflection 2. Some particles were deflected at large angles (90° or more) 3. Very few particles (1 in 8000) were scattered back at 180° 4.

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1. **Stability Problem**: According to classical theory, accelerated electrons should emit electromagnetic radiation, lose energy, and spiral into the nucleus 2. **Continuous Spectrum Problem**: The m

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Electrons move in circular orbits around the nucleus with centripetal force provided by Coulomb force: **Formula**: mv²/r = (1/4πε₀) × (Ze²/r²) Where: - m = mass of electron - v = velocity of electr

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Only those circular orbits are allowed for which orbital angular momentum is an integral multiple of h/2π: **Formula**: L = mvr = nh/2π Where: - L = orbital angular momentum - n = principal quantum

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**Third Postulate**: Electrons in allowed orbits do not radiate energy. These are called stationary states. **Fourth Postulate**: Energy is emitted/absorbed when electrons transition between energy l

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**Given**: Bohr's postulates **Step 1**: From force balance: mv²/r = ke²/r² ... (1) **Step 2**: From quantization: mvr = nh/2π ... (2) **Step 3**: From (2): v = nh/2πmr **Step 4**: Substitute in (1):

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**Bohr radius (a₀)**: Radius of first orbit of hydrogen atom (n=1) **Formula**: a₀ = h²ε₀/πme² **Given values**: - h = 6.626 × 10⁻³⁴ J·s - ε₀ = 8.854 × 10⁻¹² C²/N·m² - m = 9.109 × 10⁻³¹ kg - e = 1.6