Category: HC Verma Part 2: Modern Physics

Problem Statement Find the series limit (shortest wavelength) of the Brackett series of hydrogen ($n \to n=4$). 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 oscillation/wave problem: Find the longest wavelength in the Paschen series of hydrogen (transition $n=4 \to n=3$). $1/\lambda = R_H(1/3^2 – 1/4^2)$ Step 1: $$\frac{1}{\lambda} = 1.097\times10^7\left(\frac{1}{9} – \frac{1}{16}\right) = 1.097\times10^7\times\frac{7}{144}$$ Step 2: $= 1.097\times10^7\times0.04861 = 5.33\times1 Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions…

Problem Statement Find the ionization energy of Li$^{2+}$ ($Z = 3$) from its ground state. 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…

Problem Statement Solve the work-energy problem: Find the ground state energy of He$^+$ (hydrogen-like helium ion, $Z = 2$). For hydrogen-like ion: $E_n = -13.6Z^2/n^2$ eV Step 1: $Z = 2$, $n = 1$: $$E_1 = -13.6\times\frac{2^2}{1^2} = -13.6\times4 = -54.4\text{ eV}$$ $$\boxed{E_1(\text{He}^+) = -54.4\text{ eV}}$$ Given Information Mass $m$, velocity $v$, height $h$, or…

Problem Statement Find the radius of the $n = 5$ orbit in hydrogen. 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…

Problem Statement How much energy is required to ionize hydrogen from the $n = 3$ state? 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…

Problem Statement Derive the Rydberg constant $R_H$ from Bohr theory. 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 the system,…

Problem Statement Solve the quantum/modern physics problem: Calculate the energy of the photon emitted when hydrogen atom transitions from $n = 4$ to $n = 2$. $E_{photon} = E_4 – E_2 = -13.6(1/4^2 – 1/2^2)$ eV wait, $E_{photon} = E_{initial} – E_{final}$ Step 1: $E_4 = -13.6/16 = -0.85$ eV; $E_2 = -13.6/4 = -3.40$…

Problem Statement Solve the work-energy problem: Find the kinetic energy, potential energy, and total energy of the electron in the $n = 2$ orbit of hydrogen. $E_n = -13.6/n^2$ eV (total) $KE_n = -E_n = 13.6/n^2$ eV $PE_n = 2E_n = -27.2/n^2$ eV Step 1: Total: $E_2 = -13.6/4 = -3.40$ eV Step 2: Kinetic:…

Problem Statement Find the frequency of revolution of the electron in the first Bohr orbit of hydrogen. 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…