Category: HC Verma Part 2: Modern Physics

Problem Statement X-rays pass through 5 mm of material with linear attenuation coefficient $\mu = 200$ m$^{-1}$. Find the percentage of intensity transmitted. 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…

Problem Statement Solve the oscillation/wave problem: A cubic crystal has lattice constant $a = 0.35$ nm. X-rays of $\lambda = 0.154$ nm are directed along a [100] direction. At what angles do (100), (200), and (110) planes give Bragg maxima (first order)? $d_{hkl} = a/\sqrt{h^2+k^2+l^2}$; Bragg: $\sin\theta = \lambda/(2d)$ (100): $d = 0.35$ nm; $\sin\…

Problem Statement The $K_\alpha$ line of an unknown element has wavelength $\lambda = 0.0794$ nm. Using Moseley’s law, find the atomic number $Z$. 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…

Problem Statement Solve the quantum/modern physics problem: An X-ray photon of energy 100 keV is Compton scattered and the scattered photon has energy 80 keV. Find the scattering angle $\theta$. $\lambda = hc/E = 1240/E[\text{eV}]$ nm; $\Delta\lambda = \lambda_C(1-\cos\theta)$ Step 1: $\lambda = 1240/100000 = 0.01240$ nm; $\lambda’ = 1240/80000 = 0.01550$ nm Given Information…

Problem Statement Solve the quantum/modern physics problem: Find the maximum energy of an X-ray photon produced when electrons accelerated through $V = 50$ kV strike a target. $E_{max} = eV$ (all kinetic energy of electron goes to one photon) Step 1: Maximum photon energy = kinetic energy of electron: Step 2: $$E_{max} = eV =…

Problem Statement X-rays of wavelength 0.071 nm (molybdenum $K_\alpha$) are used to study a KBr crystal ($d = 0.334$ nm). Find the first-order glancing 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…

Problem Statement Solve the oscillation/wave problem: A crystal with interplanar spacing $d = 0.28$ nm shows Bragg reflection of X-rays at $\theta = 10°$ for the first order. Calculate the X-ray wavelength and its frequency. $\lambda = 2d\sin\theta$; $f = c/\lambda$ Step 1: $\sin10° = 0.1736$ Step 2: $\lambda = 2\times0.28\times0.1736 = 0.09722$ nm Ste…

Problem Statement Solve the quantum/modern physics problem: X-rays of wavelength 0.02 nm undergo Compton scattering at $\theta = 180°$. Find the kinetic energy of the recoil electron. $\Delta\lambda = 2\lambda_C = 0.00486$ nm $KE_e = E_{photon} – E’_{photon}$ Step 1: $\lambda’ = 0.02 + 0.00486 = 0.02486$ nm Step 2: $E = 1240/0.02 = 62000$…

Problem Statement Solve the work-energy problem: For a target with $K$-shell binding energy $E_K = -25$ keV and $L$-shell $E_L = -3$ keV, find the wavelength of the $K_\alpha$ X-ray. $E_{K\alpha} = E_K – E_L$ (energy of emitted photon); $\lambda = hc/E$ Step 1: $E_{K\alpha} = |E_K – E_L| = |-25 – (-3)| = 22$…

Problem Statement The linear attenuation coefficient for X-rays in a material is $\mu = 50$ cm$^{-1}$. Find the half-value layer (HVL) thickness that reduces intensity to half. 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…