Category: Part 6: Atomic & Nuclear

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: Find the de Broglie wavelength of a 1.0 g marble at 1.0 m/s. $$\lambda = h/(mv) = 6.626\times10^{-34}/(10^{-3}\times1) = 6.6\times10^{-31} \text{ m}$$ This is $\sim10^{16}$ times smaller than a proton. Wave effects are completely unobservable for macroscopic Given Information Mass $m$ and spring constant…

Problem Statement Solve the quantum/modern physics problem: Derive $\Delta\lambda = (h/m_ec)(1-\cos\theta)$ from energy and momentum conservation. From energy and 2D momentum conservation, eliminating the electron angle: $$p_e^2c^2 = E_0^2 + E’^2 – 2E_0E’\cos\theta$$ Energy conservation: $E_e = E_0 – E’ + m_ec^2$. Using $E_e^2 = p_e^2c^2 + m_e^2c^4$: $$(E_0- Given Information All quantities, constants, and…

Problem Statement Solve the fluid mechanics problem: Solve the fluid mechanics problem: Find radiation pressure of sunlight ($I = 1360$ W/m²) on an absorbing surface. $$P_{rad} = I/c = 1360/3\times10^8 = 4.53\times10^{-6} \text{ Pa} = 4.53 \mu\text{Pa}$$ For a perfectly reflecting surface: $P = 2I/c \approx 9.1\mu$Pa. Fluid density $\rho$, velocities, Given Information Fluid density…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the gravitation problem: Compare the electric and gravitational forces on the electron in the first Bohr orbit. $$F_e = e^2/(4\pi\varepsilon_0r_1^2) = 9\times10^9\times(1.6\times10^{-19})^2/(0.529\times10^{-10})^2 = 8.2\times10^{-8} \text{ N}$$ $$F_g = Gm_em_p/r_1^2 = 6.67\times10^{-11}\times9 Given Information Mass(es), forces, angles, and coefficients of friction as given $g = 9.8\,\text{m/s}^2$…

Problem Statement Find the minimum photon energy for electron-positron pair production near a nucleus. 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…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: Find $V_s$ for Na ($\phi = 2.27$ eV) at $\lambda = 200$ nm and 300 nm. 200 nm: $V_s = 1240/200 – 2.27 = 6.20-2.27 = 3.93$ V 300 nm: $V_s = 1240/300 – 2.27 = 4.13-2.27 = 1.86$ V Frequency $\nu$ or wavelength…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Fine structure splitting of hydrogen $2p$: $\Delta E = 4.5\times10^{-5}$ eV. Find $B_{eff}$. $$B_{eff} = \Delta E/(2\mu_B) = 4.5\times10^{-5}\times1.6\times10^{-19}/(2\times9.274\times10^{-24}) = 0.39 \text{ T}$$ Answer: $B_{eff} \approx 0.4$ T (effective inte Given Information Current $I$ or charge $q$ and velocity $v$ as given Geometry…

Problem Statement Electrons with $\lambda = 0.10$ nm pass through slits separated $d = 1.0$ μm. Find the first maximum angle. 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 Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Find the centripetal acceleration of the electron in the first Bohr orbit. $$a = v_1^2/r_1 = (2.19\times10^6)^2/0.529\times10^{-10} = 9.07\times10^{22} \text{ m/s}^2$$ This enormous acceleration ($\sim10^{22}g$) would classically cause radiation and orbit Given Information Mass(es), forces, angles, and coefficients of…

Problem Statement Find the splitting of $\lambda = 500$ nm in field $B = 1.0$ T. 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…