## Numerical

In a radioactive decay chain reaction, ${ }_{90}^{230} \mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \mathrm{Po}$ nucleus. The ratio of the number ...

Suppose a $$_{88}^{226}Ra$$ nucleus at rest and in ground state undergoes $$\alpha $$-decay to a $$_{86}^{222}Rn$$ nucleus in its excited state. The k...

Consider a hydrogen-like ionized atom with atomic number $$Z$$ with a single electron. In the emission spectrum of this atom, the photon emitted in th...

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number $${n_i}$$ to another with quantum number $${n_f}$$. $${V_i}$$ ...

$${}^{131}{\rm I}$$ is an isotope of Iodine that $$B$$ decays to an isotope of Xenon with a half-life of $$8$$ days. A small amount of a serum labell...

A hydrogen atom in its ground state is irradiated by light of wavelength 970$$\mathop A\limits^o $$.Taking hc/e = 1.237 $$\times$$ 10$$-$$6 eVm and t...

The isotopes $$_5^{12}B$$ having a mass 12.014 u undergoes $$\beta $$-decay to $$_6^{12}C$$. $$_6^{12}C$$ has an excited state of the nucleus ($$_6^{1...

For a radioactive material, its activity A and rate of change of its activity R are defined as $$A = - {{dN} \over {dt}}$$ and $$R = - {{dA} \over {...

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 ...

Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kin...

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the ...

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln2 = 0.693, the fraction of t...

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...

To determine the half-life of a radioactive element, a student plots a graph of $$\ln \left| {{{dN(t)} \over {dt}}} \right|$$ versus t. Here, $${{dN(t...

## MCQ (More than One Correct Answer)

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed insi...

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is ...

A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive
constant and r is its distance from the origin. I...

A free hydrogen atom after absorbing a photon of wavelength $$\lambda $$a gets excited from the state n = 1 to the state n = 4. Immediately after that...

In a radioactive decay chain, $${}_{90}^{232}Th$$ nucleus decays to $${}_{82}^{212}Pb$$ nucleus. Let $${N_\alpha }$$ and $${N_\beta }$$ be the number ...

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, whe...

A fission reaction is given by $$_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y$$, where x and y are two particles. Considering $$_{92}^{236}U$...

The radius of the orbit of an electron in a hydrogen-like atom is 4.5a0, where a0 is the Bohr radius. Its orbital angular momentum is $${{3h} \over {2...

## MCQ (Single Correct Answer)

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number ...

In a radioactive sample, $${}_{19}^{40}K$$ nuclei either decay into stable $${}_{20}^{40}Ca$$ nuclei with decay constant 4.5 $$ \times $$ 10-10 per ye...

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tes...

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by $$E = {3 \over 5}{{Z(Z - 1){e^2}} \...

Match the nuclear processes given in Column I with the
appropriate option(s) in Column II:
...

If $$\lambda$$Cu is the wavelength of K$$\alpha$$ X-ray line of copper (atomic number 29) and $$\lambda$$Mo is the wavelength of the K$$\alpha$$ X-ray...

The correct statement is

The kinetic energy (in keV) of the alpha particle, when the nucleus $$_{84}^{210}Po$$ at rest undergoes alpha decay, is

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct a...

What is the maximum energy of the anti-neutrino?

If the anti-neutrino had a mass of 3 eV/c2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of...

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 $$\mathop A\limits^o $$. The wavelength of the second spectral...

A diatomic molecule has moment of inertia I. By Bohr's quantization condition, its rotational energy in the nth level (n = 0 is not allowed) is

It is found that the excitation frequency from ground to the first excited stat of rotation for the CO molecule is close to $${4 \over \pi } \times {1...

In a CO molecule, the distance between C (mass = 12 amu) and O (mass = 16 amu), where 1 amu $$ = {5 \over 3} \times {10^{ - 27}}$$ kg, is close to...