A particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the $n^{\text {th }}$ orbit and the particle's speed $v$ in the orbit depend on $n$ as

The spectral series which corresponds to the electronic transition from the levels $$n_2=5,6, \ldots$$ to the level $$n_1=4$$ is

Water is used as a coolant in a nuclear reactor because of its

Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then :

Select the correct statements among the following :

A. Slow neutrons can cause fission in $${ }_{92}^{235} \mathrm{U}$$ than fast neutrons.

B. $$\alpha$$-rays are Helium nuclei.

C. $$\beta$$-rays are fast moving electrons or positrons.

D. $$\gamma$$-rays are electromagnetic radiations of wavelengths larger than $$\mathrm{X}$$-rays.

Choose the most appropriate answer from the options given below :

Given below are two statements:

Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges.

Statement II: Atoms of each element are stable and emit their characteristic spectrum.

In the light of the above statements, choose the most appropriate answer from the options given below.

Match List I with List II:

Choose the correct answer from the options given below:

$$ { }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q $$

In the nuclear emission stated above, the mass number and atomic number of the product $$Q$$ respectively, are

The ground state energy of hydrogen atom is $$-13.6 ~\mathrm{eV}$$. The energy needed to ionize hydrogen atom from its second excited state will be :

The wavelength of Lyman series of hydrogen atom appears in:

The angular momentum of an electron moving in an orbit of hydrogen atom is $$\mathrm{1.5\left(\frac{h}{\pi}\right)}$$. The energy in the same orbit is nearly.

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $$\left(\frac{1}{16}\right)^{\text {th }}$$ of its initial value?

In hydrogen spectrum, the shortest wavelength in the Balmer series is $$\lambda$$. The shortest wavelength in the Bracket series is :

The radius of inner most orbit of hydrogen atom is $$5.3 \times 10^{-11} \mathrm{~m}$$. What is the radius of third allowed orbit of hydrogen atom?

Let R₁ be the radius of the second stationary orbit and R₂ be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $${{{R_1}} \over {{R_2}}}$$ is :

Given below are two statements

Statement I : The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.

Statement II : The half of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t = 0.

In the light of the above statements, choose the most appropriate answer from the options given below :

At any instant, two elements X₁ and X₂ have same number of radioactive atoms. If the decay constant of X₁ and X₂ are 10 $$\lambda$$ and $$\lambda$$ respectively, then the time when the ratio of their atoms becomes $${1 \over e}$$ respectively will be :

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $$\times$$ 10³⁹. The ratio of the proportionality constant, $$K = {1 \over {4\pi {\varepsilon _0}}}$$ to the gravitational constant G is nearly (Given that the charge of the proton and electron each = 1.6 $$\times$$ 10^$$-$$19 C, the mass of the electron = 9.11 $$\times$$ 10^$$-$$31 kg, the mass of the proton = 1.67 $$\times$$ 10^$$-$$27 kg) :

The graph which shows the variation of the de Broglie wavelength ($$\lambda$$) of a particle and its associated momentum (p) is

In the given nuclear reaction, the element X is

$${}_{11}^{22}Na \to X + {e^ + } + v$$

Let T₁ and T₂ be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to the Bohr's model of an atom, the ratio T₁ : T₂ is

A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is