Category: HC Verma Part 2: Modern Physics

Problem Statement Solve the quantum/modern physics problem: The work function of tungsten is $\phi = 4.5$ eV. Find the minimum temperature at which thermionic emission begins, using the classical condition $kT \approx \phi$. $kT = \phi \Rightarrow T = \phi/k$ $k = 8.62\times10^{-5}$ eV/K Step 1: $$T = \frac{\phi}{k} = \frac{4.5\text{ eV}}{8.62\times10^{-5}\t Given Information See…

Problem Statement In a neon discharge tube, the positive column has current $I = 10$ mA and cross-sectional area $A = 1$ cm$^2$. The neon ion density in the positive column is $n_i = 10^{16}$ m$^{-3}$. Find the drift velocity of neon ions. Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement Solve the thermodynamics problem: A gas discharge tube contains hydrogen at pressure $p = 0.05$ mmHg. The tube length is $L = 20$ cm. Estimate the approximate mean free path and comment on whether a glow discharge is likely at this pressure. Mean free path: $\ell \approx \frac{kT}{\sqrt{2}\pi d^2 p}$ where $d \sim…

Problem Statement In a Millikan-type experiment, a droplet of mass $m = 3.3\times10^{-15}$ kg carrying charge $q$ is held stationary in an upward electric field $E = 6\times10^5$ V/m. Find the charge $q$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario…

Problem Statement Solve the magnetic field/force problem: Find the cyclotron frequency of an electron in a magnetic field of $B = 0.1$ T. Cyclotron frequency: $f_c = eB/(2\pi m_e)$ Step 1: $$f_c = \frac{eB}{2\pi m_e} = \frac{1.6\times10^{-19}\times0.1}{2\pi\times9.1\times10^{-31}}$$ Step 2: Numerator: $1.6\times10^{-20}$; Denominator: $2\pi\times9.1\times1 Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement Determine the electric field for the configuration described: An electron is held in equilibrium between gravity and an upward electric force. Find the electric field required. ($m_e = 9.1\times10^{-31}$ kg) Equilibrium: $eE = m_e g$ Step 1: $$E = \frac{m_e g}{e} = \frac{9.1\times10^{-31}\times9.8}{1.6\times10^{-19}}$$ Step 2: $$E = \frac{8.92\times10^{-30}}{1 Given Information See problem statement…

Problem Statement In a CRT experiment, electrons are accelerated through $V = 2000$ V. They then enter a transverse magnetic field $B = 5\times10^{-3}$ T. Find the radius of the circular path. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement In a plasma with electron number density $n = 10^{18}$ m$^{-3}$ and temperature $T = 10^4$ K, estimate the Debye shielding length $\lambda_D$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation…

Problem Statement In a gas discharge tube, the current density is $J = 1$ A/m² and the electron number density is $n = 10^{18}$ m$^{-3}$. Find the drift velocity of electrons. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement Analyze the circuit: In a vacuum diode, the anode voltage is $V = 250$ V and anode current is $I = 50$ mA. If the anode voltage is doubled to 500 V, find the new current. (Child’s law: $I \propto V^{3/2}$) Child-Langmuir law: $I = kV^{3/2}$ Step 1: $$\frac{I_2}{I_1} = \left(\frac{V_2}{V_1}\right)^{3/2} = \left(\frac{500…