Category: HC Verma Part 2: Modern Physics

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: A 100 W sodium vapour lamp emits monochromatic light at $\lambda = 589$ nm. Assuming 10% efficiency (electrical to light), find the number of photons emitted per second. $N = P_{light}/(hf) = P_{light}\lambda/(hc)$ Step 1: Light output power: $P_{light} = 0. Given Information…

Problem Statement Analyze the circuit: Solve the quantum/modern physics problem: In a photoelectric experiment, the stopping potential for $\lambda = 300$ nm light is $V_1 = 1.85$ V. If the wavelength is changed to $\lambda = 400$ nm, find the new stopping potential. (Work function can be calculated from first measurement.) $eV_s = hc/\l Given…

Problem Statement Solve the kinematics problem: Ultraviolet light of wavelength $\lambda = 180$ nm is incident on a lithium surface (work function $\phi = 2.5$ eV). Find the maximum speed of emitted electrons. $KE_{max} = hc/\lambda – \phi = \frac{1}{2}m_e v_{max}^2$ Step 1: Photon energy: $E_{ph} = 1240/180 = 6.89$ eV Step 2: $KE_{max} =…

Problem Statement Analyze the circuit: Analyze the circuit: A photocell uses a surface of work function $\phi = 1.9$ eV and is illuminated by light of wavelength $\lambda = 400$ nm and intensity $I = 2$ W/m². The cell has area $A = 1$ cm$^2$. If quantum efficiency (fraction of photons causing emission) is $\eta…

Problem Statement Solve the oscillation/wave problem: Solve the quantum/modern physics problem: Light of wavelength 200 nm falls on an aluminium surface (work function $\phi = 4.2$ eV). Find the de Broglie wavelength of the fastest emitted photoelectrons. $KE_{max} = hc/\lambda – \phi$ $\lambda_{dB} = h/p = h/\sqrt{2m_eKE}$ Step 1: Photon energy: $E_{p Given Information Mass…

Problem Statement Solve the quantum/modern physics problem: Solve the oscillation/wave problem: The photoelectric threshold wavelength for a metal is $\lambda_0 = 540$ nm. Find the work function of the metal. $\phi = hc/\lambda_0$ $hc = 1240$ eV·nm Step 1: $$\phi = \frac{hc}{\lambda_0} = \frac{1240\text{ eV·nm}}{540\text{ nm}} = 2.30\text{ eV}$$ $$\boxed{\ph Given Information $\phi = \frac{hc}{\lambda_0}…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: In a photoelectric experiment, the stopping potential is $V_s = 1.0$ V for light of $\lambda_1 = 250$ nm and $V_s = 0.5$ V for $\lambda_2 = 350$ nm. Find Planck’s constant $h$ and the work function $\phi$. $eV_s = hc/\lambda – \phi$;…

Problem Statement Solve the quantum/modern physics problem: When light of frequency $f = 8\times10^{14}$ Hz falls on a metal surface of work function $\phi = 1.6$ eV, find the stopping potential. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental ph…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Light of wavelength $\lambda = 300$ nm falls on a metal with work function $\phi = 2.0$ eV. Find the maximum kinetic energy of emitted photoelectrons. Einstein’s photoelectric equation: $KE_{max} = hf – \phi = hc/\lambda – \phi$ Step 1: Photon energy: $$E_{ph} = \frac{…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: The work function of sodium is $\phi = 2.3$ eV. Find the threshold frequency $f_0$ below which no photoelectric emission occurs. $\phi = hf_0 \Rightarrow f_0 = \phi/h$ $h = 6.626\times10^{-34}$ J·s $= 4.136\times10^{-15}$ eV·s Step 1: $$f_0 = \frac{\phi}{h} Given Information See…