Dual Nature of Radiation

A hydrogen atom, initially at rest in its ground state, absorbs a photon of frequency $v_1$ and ejects the electron with a kinetic energy of 10 eV . The electron then combines with a positron at rest to form a positronium atom in its ground...

Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$, a neutron having thermal energy $k_{\mathrm{B}} T$ has the same de Broglie wavelength as that of this electron. If this tem...

A metal target with atomic number $Z=46$ is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio $r$ of the wavelengths of the $K_\alpha$-line and the cut-off is found to be $r=2$. If the...

A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of th...

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0 \mathrm{~V}$. This potential drops to $0.6 \mathrm{~V}$ if another source with wavelength four times...

In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals P, Q and R are EP, EQ and ER, respectively, and they are related by EP = 2EQ = 2ER. In this experiment, the same source of monochromatic light is used...

A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency \(\Omega\) such that \({{4\pi M\Omega } \over h} = {10^{24}}{m^{ - 2}}\) with h as Planck's constant. N photons of wavelength...

In a photoelectric experiment a parallel beam of monochromatic light with power of \(200\) \(W\) is incident on a perfectly absorbing cathode of work function \(6.25\) \(ev.\) The frequency of light is just above the threshold frequency so ...

A photoelectric material having work-function \({\phi _0}\) is illuminated with light of wavelength \(\lambda \left( {\lambda < {{he} \over {{\phi _0}}}} \right).\) The fastest photoelectron has a de-Broglic wavelength \({\lambda _d}.\) A ...

Light of wavelength \(\lambda\)ph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is \(\phi\) and the anode is a wire mesh of conducting material kept at a distance d from the c...

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for th...

An electron in an excited state of Li2+ ion has angular momentum \({{3h} \over {2\pi }}\). The de Broglie wavelength of the electron in this state is p\(\pi\)a0 (where a0 is the Bohr radius). The value of p is

For photo-electric effect with incident photon wavelength \(\lambda\), the stopping potential is V0. Identify the correct variation(s) of V0 with \(\lambda\) and \({1 \over \lambda }\).

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 u1 and u2, respectively. If the ratio u1 : u2 = 2 : 1 and hc = 1240 eV n...

Using the expression \(2d\sin \theta = \lambda\), one calculates the values of d by measuring the corresponding angles \(\theta\) in
the range 0 to 90o. The wavelength \(\lambda\) is exactly known and the error in \(\theta\) is constan...

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 ___...

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 acquire...

The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10\(-\)25 kg. The mass (in mg) of the radioactive sample is _________.

An \(\alpha\)-particle and a proton are accelerated from the rest by a potential difference of 100 V. After this, their de Broglie wavelengths are \(\lambda\)\(\alpha\) and \(\lambda\)p, respectively. The ratio $${{{\lambda _p}} \over {{\la...

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions \(\phi_p=2.0~\mathrm{eV}\), \(\phi_q=2.5~\mathrm{eV}\) and \(\phi_r=3.0~\mathrm{eV}\), respecticely. A light beam containing ...

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 allowed energy for the particle for a particular value of \(n\) is proportional to

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

Electrons with de-Broglie wavelength \(\lambda\) fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

Statement 1 :
If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.

Statement 2 :
When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is c...

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 \(\times\) 4 matrix given in the ORS.

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The graph between $\frac{1}{\lambda}$ and stopping potential (V) of three metals having work functions $\phi_1, \phi_2$, and $\phi_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following stateme...

The potential energy of a particle of mass m
is given by
$$\mathrm{U}(x)=\left\{\begin{array}{cc}\mathrm{E}_{0} & 0 \leq x \leq 1 \\ 0 & x>1\end{array}\right.$$
\(\lambda_{1}\) and \(\lambda_{2}\) are the de Broglie wavelengths of the part...