An alternating voltage of amplitude $$40\mathrm{V}$$ and frequency $$4\mathrm{kHz}$$ is applied directly across the capacitor of $$12\mu \mathrm{F}$$. The maximum displacement current between the plates of the capacitor is nearly :

A series LCR circuit is subjected to an ac signal of $$200\mathrm{V},50\mathrm{Hz}$$. If the voltage across the inductor $$(\mathrm{L}=10\mathrm{mH})$$ is $$31.4\mathrm{V}$$, then the current in this circuit is _______.

Given below are two statements : Statement I : In an LCR series circuit, current is maximum at resonance. Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below :

From the statements given below : (A) The angular momentum of an electron in $n^{\text{th }}$ orbit is an integral multiple of $\hslash$. (B) Nuclear forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

The atomic mass of $${}_6{\mathrm{C}}^{12}$$ is $$12.000000\mathrm{u}$$ and that of $${}_6{\mathrm{C}}^{13}$$ is $$13.003354\mathrm{u}$$. The required energy to remove a neutron from $${}_6{\mathrm{C}}^{13}$$, if mass of neutron is $$1.008665\mathrm{u}$$, will be :

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

If the wavelength of the first member of Lyman series of hydrogen is $$\lambda$$. The wavelength of the second member will be

The explosive in a Hydrogen bomb is a mixture of $${}_1{\mathrm{H}}^2,{}_1{\mathrm{H}}^3$$ and $${}_3{\mathrm{Li}}^6$$ in some condensed form. The chain reaction is given by $$\begin{array}{rl}& {}_3{\mathrm{Li}}^6+{}_0{\mathrm{n}}^1\to {}_2{\mathrm{He}}^4+{}_1{\mathrm{H}}^3\\ & {}_1{\mathrm{H}}^2+{}_1{\mathrm{H}}^3\to {}_2{\mathrm{He}}^4+{}_0{\mathrm{n}}^1\end{array}$$ During the explosion the energy released is approximately [Given ; $$\mathrm{M}(\mathrm{Li})=6.01690\mathrm{amu},\mathrm{M}\left({}_1{\mathrm{H}}^2\right)=2.01471\mathrm{amu},\mathrm{M}\left({}_2{\mathrm{He}}^4\right)=4.00388$$ $$\mathrm{amu}$$, and $$1\mathrm{amu}=931.5\mathrm{MeV}]$$

Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate from the options given below

An electron revolving in $$n^{\text{th }}$$ Bohr orbit has magnetic moment $${\mu }_n$$. If $${\mu }_n\propto n^x$$, the value of $$x$$ is

In a nuclear fission reaction of an isotope of mass $$M$$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $$\Delta M$$ will be :

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is :

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2:1$$. After disintegration they will move :

The energy released in the fusion of $$2\mathrm{kg}$$ of hydrogen deep in the sun is $$E_H$$ and the energy released in the fission of $$2\mathrm{kg}$$ of $${}^{235}\mathrm{U}$$ is $$E_U$$. The ratio $$\frac{E_H}{E_U}$$ is approximately: (Consider the fusion reaction as $$4_1^{1}H+2{\mathrm{e}}^{-}\to {}_2^4\mathrm{He}+2v+6\gamma +26.7\mathrm{MeV}$$, energy released in the fission reaction of $${}^{235}\mathrm{U}$$ is $$200\mathrm{MeV}$$ per fission nucleus and $${\mathrm{N}}_{\mathrm{A}}=6.023\times 10^{23})$$

A hydrogen atom in ground state is given an energy of $$10.2\mathrm{eV}$$. How many spectral lines will be emitted due to transition of electrons?

The energy equivalent of $$1\mathrm{g}$$ of substance is :

Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\left({}_0^1\mathrm{n}\right)$$ and uranium isotope $$\left({}_{92}^{235}\mathrm{U}\right)$$ is correct :

According to Bohr's theory, the moment of momentum of an electron revolving in $$4^{\text{th }}$$ orbit of hydrogen atom is: