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Physics · Ch 8 — Atomic and Nuclear Physics

Summary

Summary

  • A device used to study the conduction of electricity through gases is known as a gas discharge tube.
  • Charge per unit mass is known as specific charge (or normalized charge), and it is independent of the gas used and of the nature of the electrodes.
  • The distance of closest approach r0r_0 is the minimum distance between an alpha particle and the centre of a nucleus, just before the alpha particle is reflected straight back by 180 degrees.
  • The impact parameter bb is the perpendicular distance between the centre of the nucleus and the direction of the alpha particle's velocity vector when it is very far from the nucleus.
  • According to the Bohr atom model, angular momentum is quantised: l=nℏl=n\hbar.
  • The radius of the nnth Bohr orbit is rn=a0n2/Zr_n=a_0n^2/Z, where a0=4πε0ℏ2/(me2)=0.529a_0=4\pi\varepsilon_0\hbar^2/(me^2)=0.529 Å is the Bohr radius (the radius of the first orbit).
  • The electron's velocity in the nnth orbit is υn=2πh⋅Ze24πε0n\upsilon_n=\dfrac{2\pi}{h}\cdot\dfrac{Ze^2}{4\pi\varepsilon_0 n}, and the dimensionless fine structure constant is α=1/137\alpha=1/137.
  • The total energy of the electron in the nnth orbit is En=−me4Z28ε02h2n2=−13.6 Z2/n2E_n=-\dfrac{me^4Z^2}{8\varepsilon_0^2h^2n^2}=-13.6\,Z^2/n^2 eV.
  • The energy required to excite an electron from a lower to a higher energy state is the excitation energy, and the corresponding potential is the excitation potential.
  • The minimum energy needed to remove an electron from an atom in its ground state is the ionization energy, and the corresponding potential is the ionization potential.
  • The wavelengths of the Lyman series lie in the ultraviolet region; those of the Balmer series lie in the visible region; and those of the Paschen and Brackett series lie in the infrared region.
  • The nucleus of element X, with atomic number ZZ and mass number AA, is represented as ZAX^{A}_{Z}X.
  • For Z>10Z>10, the nuclear radius follows R=R0A1/3R=R_0A^{1/3}, with R0=1.2R_0=1.2 F.
  • Nuclear density is ρ≈2.3×1017 kg m−3\rho\approx2.3\times10^{17}\ \text{kg m}^{-3} for every nucleus with Z>10Z>10.
  • If MM, mpm_p and mnm_n are the masses of a nucleus ZAX^{A}_{Z}X, a proton and a neutron respectively, the mass defect is Δm=(Zmp+Nmn)−M\Delta m=(Zm_p+Nm_n)-M.
  • The binding energy of a nucleus is BE=[Zmp+Nmn−M]c2BE=[Zm_p+Nm_n-M]c^2.
  • The binding energy per nucleon is maximum for iron, at 8.8 MeV.
  • Alpha decay: ZAX→Z−2A−4Y+24He^{A}_{Z}X\to{}^{A-4}_{Z-2}Y+{}^{4}_{2}He. Beta-minus decay: ZAX→Z+1AY+e−+νˉ^{A}_{Z}X\to{}^{A}_{Z+1}Y+e^-+\bar\nu. Beta-plus decay: ZAX→Z−1AY+e++ν^{A}_{Z}X\to{}^{A}_{Z-1}Y+e^++\nu. Gamma decay: ZAX∗→ZAX+γ^{A}_{Z}X^{*}\to{}^{A}_{Z}X+\gamma. …
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