Atoms and Nuclei · Physics · JEE Advanced

A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r)=-k r$, corresponding to the potential energy $V(r)...

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

A heavy nucleus N, at rest, undergoes fission N $$\to$$ P + Q, where P and Q are two lighter nuclei. Let $$\delta$$ = MN $$-$$ MP $$-$$ MQ, where MP, ...

Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?

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...

Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(...

In a radioactive decay process, the activity is defined as $A=-\frac{d N}{d t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two rad...

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

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}^{16} \mathrm{~N}+$ ${ }_{2}^{4} \mathrm{He} \rightarrow{...

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 = 1.237 $$\times$$ 10$$-$$6 eVm and the...

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

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 {...

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...

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...

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate ent...

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 state of rotation for the CO molecule is close to $${4 \over \pi } \times {...

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 :...

The speed of the particle, that can take discrete values, is proportional to

In the core of nuclear fusion reactor, the gas becomes plasma because of

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 kT, when th...

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on L...

A radioactive sample S1 having activity of 5 $$\mu$$Ci has twice the number of nuclei as another sample S2 which has an activity of 10 $$\mu$$Ci. The ...

The quantum number n of the state finally populated in He$$^+$$ ions is :

The wavelength of light emitted in the visible region by He$$^+$$ ions after collisions with H atoms is

The ratio of the kinetic energy of the $$n=2$$ electron for the H atom to that of He$$^+$$ ion is