Dual Nature of Radiation and Matter

An electron in an excited state of $\ce{Li^{2+}}$ ion has angular momentum $3h/2\pi$. The de Broglie wavelength of the electron in this state is $p\pi a_0$ (where $a_0$ is the Bohr radius). The value of $p$ is

Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list :

A parallel beam of electrons travelling in $x$-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum $p_y$ in the $y$-direction then for a majority of electrons passing through the slit (h is Planck's constant) :

de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to ($|e|=1.6\times10^{-19}$ C, $m_e=9.1\times10^{-31}$ kg, $h=6.6\times10^{-34}$ Js) :

The de - Broglie wavelength associated with the electron in the n = 4 level is :

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are $u_1$ and $u_2$, respectively. If the ratio $u_1:u_2=2:1$ and $hc=1240$ eV nm, the work function of the metal is nearly

The radiation corresponding to $3\to2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times10^{-4}$ T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship ?

A photon of wavelength $\lambda$ is scattered from an electron, which was at rest. The wavelength shift $\Delta\lambda$ is three times of $\lambda$ and the angle of scattering $\theta$ is 60°. The angle at which the electron recoiled is $\phi$. The value of $\tan\phi$ is : (electron speed is much smaller than the speed of light)

A beam of light has two wavelengths 4972 Å and 6216 Å with a total intensity of $3.6\times10^{-3}$ Wm$^{-2}$ equally distributed among the two wavelengths. The beam falls normally on an area of 1 cm$^2$ of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photo electrons liberated in 2s is approximately :

Match List - I (Experiment performed) with List - II (Phenomena discovered/associated) and select the correct option from the options given below the lists :

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is $3\times10^8\ \mathrm{m\,s^{-1}}$. The final momentum of the object is

The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is

A proton is fired from very far away towards a nucleus with charge $Q=120e$, where $e$ is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is: (take the proton mass, $m_p=(5/3)\times10^{-27}$ kg; $h/e=4.2\times10^{-15}$ J.s/C; $\dfrac1{4\pi\varepsilon_0}=9\times10^9$ m/F; 1 fm $=10^{-15}$ m)

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $A\times10^{Z}$ (where $1<A<10$). The value of '$Z$' is

An $\alpha$-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are $\lambda_\alpha$ and $\lambda_p$ respectively. The ratio $\dfrac{\lambda_p}{\lambda_\alpha}$, to the nearest integer, is

The allowed energy for the particle for a particular value of $n$ is proportional to

If the mass of the particle is $m=1.0\times10^{-30}$ kg and $a=6.6$ nm, the energy of the particle in its ground state is closest to

The speed of the particle, that can take discrete values, is proportional to

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions $\phi_p=2.0$ eV, $\phi_q=2.5$ eV and $\phi_r=3.0$ eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is [Take $hc=1240$ eV nm]