Category: HC Verma Part 2: Modern Physics

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: A bullet of mass $m = 0.05$ kg moves at $v = 300$ m/s. If the momentum uncertainty is $\Delta p/p = 10^{-6}$, find the minimum uncertainty in position $\Delta x$. $\Delta x \geq \hbar/(2\Delta p)$ Step 1: $p = mv = 0.05\times300…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: In Young’s double slit experiment with electrons, the slit separation is $d = 0.1$ mm and the screen distance is $D = 1$ m. Electrons are accelerated through $V = 100$ V. Find the fringe width. $\lambda = 1.226/\sqrt{V}$ nm; fringe width $\beta = \lambda…

Problem Statement Solve the momentum/collision problem: Solve the quantum/modern physics problem: A laser beam of power $P = 10$ mW and wavelength $\lambda = 630$ nm is reflected normally from a mirror. Find the force exerted on the mirror. Force on reflecting surface: $F = 2P/c$ (momentum reversal doubles impulse) Step 1: For perfect reflection,…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: In a photoelectric experiment, a retarding potential of $V = 2.5$ V just stops the photoelectric current. If the frequency of incident light is $f = 9\times10^{14}$ Hz, find the work function. $eV_s = hf – \phi \Rightarrow \phi = hf – eV_s$…

Problem Statement Solve the work-energy problem: Solve the quantum/modern physics problem: An atom emits a photon of wavelength $\lambda = 500$ nm. The lifetime of the excited state is $\tau = 10^{-8}$ s. Find the natural linewidth $\Delta\lambda$ of the emitted light. $\Delta E \cdot \Delta t \geq \hbar$; $\Delta E \approx \hbar/\tau$ $\Delta\lam Given…

Problem Statement Solve the momentum/collision problem: Solve the quantum/modern physics problem: An electron is confined to a region of size $\Delta x = 1$ nm. Estimate the minimum uncertainty in its momentum and the corresponding minimum kinetic energy. $\Delta x \cdot \Delta p \geq \hbar/2$; use $\Delta p \approx \hbar/\Delta x$ Step 1: $\hbar =…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: Find the de Broglie wavelength of a proton ($m_p = 1.67\times10^{-27}$ kg) moving at $v = 10^6$ m/s. $\lambda = h/(m_p v)$ Step 1: $$\lambda = \frac{h}{m_p v} = \frac{6.626\times10^{-34}}{1.67\times10^{-27}\times10^6} = \frac{6.626\times10^{-34}}{1.67\times1 Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: Find the de Broglie wavelength of an electron accelerated through a potential difference of $V = 100$ V. $KE = eV = p^2/(2m)$; $\lambda = h/p = h/\sqrt{2m_eV_e\cdot e}$ Shortcut: $\lambda = 1.226/\sqrt{V}$ nm for electrons (V in volts) Step 1: $$\lambda = \f…

Problem Statement Solve the quantum/modern physics problem: Find the maximum Compton shift in wavelength (at $\theta = 180°$) and the fractional change in energy of the scattered X-ray photon (incident $\lambda = 0.05$ nm). $\Delta\lambda_{max} = 2\lambda_C = 4.86\times10^{-12}$ m $= 0.00486$ nm Fractional energy change: $\Delta E/E = \Delta\lambda/\lambda’$ Given Information All quantities, constants,…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: X-rays of wavelength $\lambda = 0.10$ nm are scattered by a target. Find the Compton wavelength shift when the scattering angle is $\theta = 90°$. Compton formula: $\Delta\lambda = \lambda_C(1-\cos\theta)$ Compton wavelength: $\lambda_C = h/(m_e c) = 2.43\ti Given Information Mass $m$ and spring…