The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as:

A radioactive nucleus ${\mathrm{n}}_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$ ?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A , for nuclei with mass numbers between 30 and 170 . Reason (R) : Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below :

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is $2000\stackrel{o}{A}$ and it becomes $6000\stackrel{o}{A}$ when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

Choose the correct nuclear process from the below options [ p : proton, n : neutron, ${\mathrm{e}}^{-}$: electron, ${\mathrm{e}}^{+}$: positron, $v:$ neutrino, $\bar{v}:$ antineutrino]

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of ${\mathrm{He}}^{+}$ion in its first excited state. (B) the energy of H atom in ground state is same as that for ${\mathrm{Li}}^{++}$ ion in its second excited state. (C) the energy of H atom in its ground state is same as that of ${\mathrm{He}}^{+}$ion for its ground state. (D) the energy of ${\mathrm{He}}^{+}$ion in its first excited state is same as that for ${\mathrm{Li}}^{++}$ion in its ground state. Choose the correct answer from the options given below :

In a hydrogen like ion, the energy difference between the $2^{\text{nd }}$ excitation energy state and ground is 108.8 eV . The atomic number of the ion is:

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

Energy released when two deuterons $\left({}_1{\mathrm{H}}^2\right)$ fuse to form a helium nucleus $\left({}_2{\mathrm{He}}^4\right)$ is : (Given : Binding energy per nucleon of ${}_1{\mathrm{H}}^2=1.1\mathrm{MeV}$ and binding energy per nucleon of ${}_2{\mathrm{He}}^4=7.0\mathrm{MeV}$ )

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of ${\mathrm{Li}}^{++}$ ion in its ground state is given by $\frac{1}{X}{a}_0$, where $X=$ __________ (Where ${\mathrm{a}}_0$ is the first Bohr's radius.)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The density of the copper ${(}_{29}^{64}\text{Cu})$ nucleus is greater than that of the carbon ${(}_6^{12}\text{C})$ nucleus. Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$. In the light of the above statements, choose the most appropriate answer from the options given below:

$$\text{ Match the LIST-I with LIST-II }$$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} List - I List - II A. $${}_0^1\mathrm{n}+{}_{92}^{235}\mathrm{U}\to {}_{54}^{140}\mathrm{Xe}+{}_{38}^{94}\mathrm{Sr}+2{}_0^1\mathrm{n}$$ I. $$\text{ Chemical reaction }$$ B. $$2{\mathrm{H}}_2+{\mathrm{O}}_2\to 2{\mathrm{H}}_2\mathrm{O}$$ II. $$\text{ Fusion with +ve }\mathrm{Q}\text{ value }$$ C. $${}_1^2\mathrm{H}+{}_1^2\mathrm{H}\to {}_2^3\mathrm{He}+{}_0^1\mathrm{n}$$ III. $$\text{ Fission }$$ D. $${}_1^1\mathrm{H}+{}_1^3\mathrm{H}\to {}_1^2\mathrm{H}+{}_1^2\mathrm{H}$$ IV. $$\text{ Fusion with -ve }Q\text{ value }$$ $$\text{ Choose the correct answer from the options given below: }$$

A radioactive material $P$ first decays into $Q$ and then $Q$ decays to non-radioactive material $R$. Which of the following figure represents time dependent mass of $P, Q$ and $R$ ?

Given below are two statements : Statement (I) : The dimensions of Planck's constant and angular momentum are same. Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below :

Considering the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{\text{th }}$ orbit of the electron in ${\mathrm{Li}}^{2+}$ and ${\mathrm{He}}^{+}$is

Given below are two statements: one is labelled as $\mathbf{Assertion}\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason $\mathbf{R}$ : The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have