Category: Part 6: Atomic & Nuclear

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Find the orbital magnetic moment of the electron in the first Bohr orbit. $\mu = evr/2 = e\hbar/(2m_e) = \mu_B$ (one Bohr magneton) $$\mu_B = e\hbar/(2m_e) = 9.274\times10^{-24} \text{ J/T}$$ The magnetic moment in the $n$-th orbit is $\mu_n = n\mu_B$. Answer: Given…

Problem Statement Show kinetic, potential, and total energy satisfy $E = U/2 = -T$ in Bohr orbits. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation…

Problem Statement Solve the nuclear physics problem: A $K_\alpha$ X-ray has $\lambda = 0.76$ Å. Find the atomic number $Z$. Moseley/Bohr for $K_\alpha$: $h\nu = \frac{3}{4}R_Hhc(Z-1)^2$ $$\nu = c/\lambda = 3\times10^8/0.76\times10^{-10} = 3.95\times10^{18} \text{ Hz}$$ $$(Z-1)^2 = \frac{4\nu}{3R_Hc} = \frac{4\times3.95\times10^{18}}{3\times1.097\times Given Information All quantities, constants, and constraints stated in the problem above Physical constants used…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: Find minimum wavelength to ionize: (a) H ground state; (b) H first excited state; (c) He$^+$ ground state. (a) $E_i = 13.6$ eV: $\lambda = 1240/13.6 = 91.2$ nm (b) $|E_2| = 3.4$ eV: $\lambda = 1240/3.4 = 364.7$ nm (c) $Z^2\times13.6 = 4\times13.6 =…

Problem Statement Solve the gravitation problem: Solve the gravitation problem: Find orbital periods for $n=1,2,3$ in hydrogen and compare to classical emission frequency. $T_n = 2\pi r_n/v_n = 2\pi n^3a_0/v_1 = n^3T_1$ $$T_1 = 2\pi a_0/v_1 = 2\pi\times0.529\times10^{-10}/2.19\times10^6 = 1.52\times10^{-16} \text{ s}$$ $T_1 = 1.52\times10^{-16}$ s Given Information Masses $M$ (planet/star) and $m$ (object/satellite) Orbital…

Problem Statement A hydrogen atom excited to $n=4$ returns to ground state. Find maximum photons from one atom and total spectral lines. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key…

Problem Statement A hydrogen atom is bombarded by an electron with $T = 12.0$ eV. Find the maximum quantum number reached. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is…

Problem Statement Find the series-limit wavelengths for Lyman, Balmer, and Paschen series. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs…

Problem Statement Find the wavelengths of the first three Balmer series lines. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Find the energies of hydrogen in states $n=1,2,3$ and photon energies for transitions $2\to1$, $3\to1$, $3\to2$. $E_n = -13.6/n^2$ eV: $E_1 = -13.6$ eV, $E_2 = -3.40$ eV, $E_3 = -1.51$ eV $2\to1$: $h\nu = 10.2$ eV, $\lambda = 121.6$ nm (Ly-$\alpha$) $3\to1$: $h\nu =…