Category: HC Verma Part 2: Modern Physics

Problem Statement X-rays of intensity $I_0$ pass through an aluminium sheet. The linear attenuation coefficient is $\mu = 100$ m$^{-1}$. Find the thickness needed to reduce intensity to $I_0/10$. 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…

Problem Statement X-rays of wavelength 0.154 nm give first-order Bragg reflection at $\theta = 27.5°$ from KCl crystal. Find the interplanar spacing and calculate Avogadro’s number if the density of KCl is $\rho = 1990$ kg/m³ and molar mass $M = 74.5$ g/mol. Given Information All quantities, constants, and constraints stated in the problem above…

Problem Statement Solve the quantum/modern physics problem: X-rays of wavelength 0.1 nm are Compton-scattered at $\theta = 90°$. Find the energy of the scattered photon. $\lambda’ = \lambda + \lambda_C = 0.1 + 0.00243 = 0.10243$ nm; $E’ = hc/\lambda’$ Step 1: $\lambda’ = 0.1 + 0.00243 = 0.10243$ nm Step 2: $$E’ = \frac{1240}{0.10243}…

Problem Statement Solve the quantum/modern physics problem: An X-ray photon of wavelength $\lambda = 0.05$ nm strikes an electron at rest. If the photon scatters at $\theta = 60°$, find the wavelength of the scattered photon. Compton: $\Delta\lambda = \lambda_C(1-\cos\theta)$; $\lambda_C = 0.00243$ nm Step 1: $\Delta\lambda = 0.00243(1-\cos60°) = 0.00243(1-0 Given Information Frequency $\nu$…

Problem Statement An element emits $K_\alpha$ X-rays of frequency $f = 2.0\times10^{18}$ Hz. Using Moseley’s law ($\sqrt{f} = 4.97\times10^7(Z-1)$), identify the element. 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 Solve the work-energy problem: An X-ray tube draws 10 mA current at 60 kV. The efficiency of X-ray production is 0.5%. Find the power input and the X-ray power output. $P_{input} = IV$; $P_{X-ray} = \eta P_{input}$ Step 1: $P_{input} = IV = 10\times10^{-3}\times60\times10^3 = 600$ W Step 2: $P_{X-ray} = 0.005\times600 =…

Problem Statement Solve the oscillation/wave problem: X-rays of wavelength $\lambda = 0.2$ nm are incident on crystal planes with $d = 0.25$ nm. Find all orders of Bragg reflection and their angles. $\sin\theta = n\lambda/(2d)$; need $\sin\theta \leq 1$, so $n \leq 2d/\lambda$ Step 1: Maximum order: $n_{max} = \lfloor 2d/\lambda\rfloor = \lfloor 2\time Given…

Problem Statement Solve the oscillation/wave problem: X-rays of wavelength $\lambda = 0.154$ nm are incident on a crystal. The second-order Bragg maximum appears at $\theta_2 = 32°$. Find the interplanar spacing $d$. $2d\sin\theta = n\lambda$; $n = 2$ Step 1: $\sin 32° = 0.5299$ Step 2: $$d = \frac{n\lambda}{2\sin\theta} = \frac{2\times0.154}{2\times0. Given Information Mass $m$…

Problem Statement Solve the oscillation/wave problem: The $K$-absorption edge of iron ($Z=26$) is at $\lambda_K = 0.174$ nm. Find the binding energy of a $K$-shell electron in iron. $E_K = hc/\lambda_K = 1240/\lambda[\text{nm}]$ eV Step 1: $$E_K = \frac{1240}{0.174} = 7126\text{ eV} \approx 7.13\text{ keV}$$ $$\boxed{E_K(\text{Fe}) \approx 7.13\text{ k Given Information Mass $m$ and spring…

Problem Statement Solve the work-energy problem: The $K_\alpha$ X-ray of molybdenum ($Z=42$) has wavelength 0.0712 nm. Find the energy of the $K_\alpha$ photon and the difference between the $K$ and $L$ shell energies. $E = hc/\lambda = 1240/\lambda[\text{nm}]$ eV; $E_{K\alpha} = E_K – E_L$ Step 1: $$E_{K\alpha} = \frac{1240}{0.0712} = 17416\text{ Given Information Mass $m$,…