The energy of $${\mathrm{He}}^{+}$$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $$-13.6\mathrm{eV})$$ :

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $${\lambda }_A$$ and $${\lambda }_B$$ are decay constants of A and B respectively, then choose the correct relation from the given options.

The half life of a radioactive substance is T. The time taken, for disintegrating $$\frac{7}{8}$$th part of its original mass will be:

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

A radio active material is reduced to $$1/8$$ of its original amount in 3 days. If $$8\times 10^{-3}\mathrm{kg}$$ of the material is left after 5 days the initial amount of the material is

The waves emitted when a metal target is bombarded with high energy electrons are

For a nucleus $${}_{\mathrm{A}}^{\mathrm{A}}\mathrm{X}$$ having mass number $$\mathrm{A}$$ and atomic number $$\mathrm{Z}$$ A. The surface energy per nucleon $$\left(b_{\mathrm{s}}\right)=-a_1{A}^{2/3}$$. B. The Coulomb contribution to the binding energy $${\mathrm{b}}_{\mathrm{c}}=-a_2\frac{Z(Z-1)}{A^{4/3}}$$ C. The volume energy $${\mathrm{b}}_{\mathrm{v}}=a_{3}A$$ D. Decrease in the binding energy is proportional to surface area. E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $$a_1,a_2$$ and $$a_3$$ are constants) Choose the most appropriate answer from the options given below:

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2}m{\omega }^2{r}^2$$ where $$\omega$$ is constant and $$r$$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $$n^{\text{th }}$$ orbit will be proportional to,

A Carnot engine operating between two reservoirs has efficiency $$\frac{1}{3}$$. When the temperature of cold reservoir raised by x, its efficiency decreases to $$\frac{1}{6}$$. The value of x, if the temperature of hot reservoir is $$99^{\circ }$$C, will be :

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point '$$\mathrm{K}$$' is :

Heat energy of $735\mathrm{J}$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{\mathrm{Cp}}{\mathrm{Cv}}$ will be.

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is $$\left(\mathrm{given},\gamma =\frac{3}{2}\right)$$ :

$$\left(P+\frac{a}{V^2}\right)(V-b)=RT$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a,b,R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^2}{a}$$, will be:

The average kinetic energy of a molecule of the gas is

The pressure of a gas changes linearly with volume from $$\mathrm{A}$$ to $$\mathrm{B}$$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

The correct relation between \gamma = {{{c_p}} \over {{c_v}}} and temperature T is :

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A: Efficiency of a reversible heat engine will be highest at $-273^{\circ }\mathrm{C}$ temperature of cold reservoir. Reason R: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta =\left(1-\frac{T_2}{T_1}\right)$ In the light of the above statements, choose the correct answer from the options given below

A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ }\mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is: