#quantum theory

De Broglie Wavelength and Matter Waves

Which scientist proposed that moving particles of matter exhibit wave-like properties?

**De Broglie wavelength** λ = h/p = h/(m v) = h/√(2 m e V) for electron accelerated through V, for V=100 V λ= h/√(2 m e×100)=1.227/√V nm=0.1227 nm, for 50 V 0.173 nm, for particle mass 3.0×10⁻³⁰ kg v=10⁶ m/s λ=6.63×10⁻³⁴/(3×10⁻³⁰×10⁶)=2.21×10⁻¹⁰ m=0.221 nm, inversely proportional to momentum, property inversely proportional to de Broglie wavelength is momentum. Louis de Broglie proposed the wave-particle duality of matter, suggesting that particles like electrons have associated wavelengths ( λ = (h/p) ). Applying E = h f = h c/λ, p = h/λ, K_max = h f - Φ, Φ = h f₀ = h c/λ₀, λ = h/√(2

Ref: NCERT > Physics Book > Dual Nature of Matter > De Broglie Wavelength and Matter Waves

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Atomic Models - Rutherford, Thomson and Bohr

Why does the Bohr model predict discrete spectral lines for hydrogen?

**Rutherford's nuclear model** atom has small massive positively charged nucleus with electrons orbiting, size ratio atomic to nuclear ~10⁵, nucleus ~10⁻¹⁵ m atom ~10⁻¹⁰ m, most alpha particles with large impact parameter pass undeflected, small fraction >90° scatter from close approach, centripetal force provided by Coulomb attraction k Z e²/r², fails to explain stability because accelerating charge should radiate and collapse. Discrete spectral lines arise because electrons transition between fixed energy levels, emitting photons with energies equal to the differences between these levels. U

Ref: NCERT > Physics Book > Atoms and Nuclei > Atomic Models - Rutherford, Thomson and Bohr

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Atomic Models - Rutherford, Thomson and Bohr

Which of the following statements is correct about the energy levels in a hydrogen atom according to Bohr’s model?

**Rutherford's nuclear model** atom has small massive positively charged nucleus with electrons orbiting, size ratio atomic to nuclear ~10⁵, nucleus ~10⁻¹⁵ m atom ~10⁻¹⁰ m, most alpha particles with large impact parameter pass undeflected, small fraction >90° scatter from close approach, centripetal force provided by Coulomb attraction k Z e²/r², fails to explain stability because accelerating charge should radiate and collapse. The energy becomes less negative (increases) as the principal quantum number n increases, approaching zero at n = ∞ . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π,

Ref: NCERT > Physics Book > Atoms and Nuclei > Atomic Models - Rutherford, Thomson and Bohr

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Atomic Models - Rutherford, Thomson and Bohr

In the Bohr model, what is the ground state of a hydrogen atom?

**Rutherford's nuclear model** atom has small massive positively charged nucleus with electrons orbiting, size ratio atomic to nuclear ~10⁵, nucleus ~10⁻¹⁵ m atom ~10⁻¹⁰ m, most alpha particles with large impact parameter pass undeflected, small fraction >90° scatter from close approach, centripetal force provided by Coulomb attraction k Z e²/r², fails to explain stability because accelerating charge should radiate and collapse. The ground state is the lowest energy state, where the electron is in the orbit with n = 1 , having an energy of -13.6 eV. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n

Ref: NCERT > Physics Book > Atoms and Nuclei > Atomic Models - Rutherford, Thomson and Bohr

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