Category: Part 6: Atomic & Nuclear

Problem Statement Solve the quantum/modern physics problem: A photon of $\lambda = 0.0600$ nm is scattered at $\theta = 120°$. Find the scattered wavelength and electron kinetic energy. (a) $\Delta\lambda = \lambda_C(1-\cos120°) = 0.00243(1.5) = 0.00364$ nm $$\lambda’ = 0.0600 + 0.00364 = 0.0636 \text{ nm}$$ (b) $T = hc(1/\lambda – 1/\lambda’) = 1240\text{ e…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: A photon of energy $E_0 = 1.00$ MeV is scattered; the wavelength changed by $\eta = 3.0\%$. Find the kinetic energy of the recoil electron. $\lambda’ = \lambda(1+\eta)$, so $E’ = E_0/(1+\eta)$. By energy conservation: $$T = E_0 – E’ = E_0 – \frac{E_0}{1+\eta…

Problem Statement Solve the quantum/modern physics problem: A photon of frequency $\nu$ is scattered at 90° by a stationary electron. Find the scattered frequency and electron kinetic energy. Compton formula at $\theta = 90°$: $\Delta\lambda = \lambda_C(1-\cos90°) = \lambda_C$ $$\lambda’ = \frac{c}{\nu} + \lambda_C \implies \nu’ = \frac{c}{c/\nu + \lambda_C} Given Information All quantities, constants,…

Problem Statement Solve the momentum/collision problem: Solve the quantum/modern physics problem: Find the momentum of a photon whose energy equals the rest energy of an electron. For a photon: $E = pc$, so $p = E/c = m_ec^2/c = m_ec$ $$p = m_ec = (9.109\times10^{-31})(3\times10^8) = 2.73\times10^{-22} \text{ kg·m/s}$$ Corresponding wavelength (Compton w Given Information…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: Illuminating a metal alternately with $\lambda_1 = 0.35$ μm and $\lambda_2 = 0.54$ μm, the maximum photoelectron velocities differ by factor $\eta = 2.0$. Find the work function. Einstein’s equation for each wavelength, with $v_1 = \eta v_2$: $$\frac{1}{2}m( Given Information Mass $m$ and…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: Find the stopping voltage for photoelectrons from a surface with $\phi = 4.47$ eV illuminated by $\lambda = 0.198$ μm radiation. $$E_{photon} = \frac{1240}{198} = 6.26 \text{ eV}$$ $$eV_s = T_{max} = 6.26 – 4.47 = 1.79 \text{ eV}$$ $$V_s = 1.79 \text{…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Find the maximum kinetic energy of photoelectrons ejected from a cesium surface ($\phi = 2.0$ eV) by light of wavelength $\lambda = 330$ nm. Einstein’s photoelectric equation: $T_{max} = h\nu – \phi = hc/\lambda – \phi$ $$E_{photon} = \frac{1240 \text{ eV·nm}}{330 \tex Given Information Mass…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: Find the threshold frequency for the photoelectric effect from metallic lithium, whose work function is $\phi = 2.39$ eV. At the threshold frequency $\nu_0$, the photon energy exactly equals the work function: $$h\nu_0 = \phi \implies \nu_0 = \frac{\phi}{h}$ Given Information Frequency $\nu$…