Atoms and Nuclei · Physics · JEE Advanced
MCQ (More than One Correct Answer)
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 $V(r)=k r^2 / 2$, where $k$ is a positive force constant and $r$ is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by $L=n \hbar$, where $\hbar=h /(2 \pi), h$ is the Planck's constant, and $n$ a positive integer. If $v$ and $E$ are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?
The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_{b}^{p}$ and the binding energy of a neutron be $E_{b}^{n}$ in the nucleus.
Which of the following statement(s) is(are) correct?
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 $${{3h} \over {2\pi }}$$. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is(are)
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(s) given below.
Numerical
[Given : atomic mass of $$_{86}^{226}Ra$$ = 226.005 u, atomic of $$_{86}^{222}Rn$$ = 222.000 u, atomic mass of $$\alpha $$ particle = 4.000 u, 1 u = 931 MeV/e2, c is speed of the light]
Taking hc = 1.237 $$\times$$ 10$$-$$6 eVm and the ground state energy of hydrogen atom as $$-$$ 13.6 eV, the number of lines present in the emission spectrum is
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 beginning is such that the total power requirement of the village is 12.5 % of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is
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 the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is __________.
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, $${{dN(t)} \over {dt}}$$ is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is __________.
MCQ (Single Correct Answer)
| List - I | List - II |
|---|---|
| (P) ${ }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa}$ | (1) one $\alpha$ particle and one $\beta^{+}$particle |
| (Q) ${ }_{82}^{214} \mathrm{~Pb} \rightarrow{ }_{82}^{210} \mathrm{~Pb}$ | (2) three $\beta^{-}$particles and one $\alpha$ particle |
| (R) ${ }_{81}^{210} \mathrm{Tl} \rightarrow{ }_{82}^{206} \mathrm{~Pb}$ | (3) two $\beta^{-}$particles and one $\alpha$ particle |
| (S) ${ }_{91}^{228} \mathrm{~Pa} \rightarrow{ }_{88}^{224} \mathrm{Ra}$ | (4) one $\alpha$ particle and one $\beta^{-}$particle |
| (5) one $\alpha$ particle and two $\beta^{+}$particles |
[Given : In 10 = 2.3]
The measured masses of the neutron, $$_1^1H$$, $$_7^{15}N$$ and $$_8^{15}O$$ are 1.008665u, 1.007825u, 15.000109u and 15.003065u, respectively. Given that the radii of both the $$_7^{15}N$$ and $$_8^{15}O$$ nuclei are same, 1 u = 931.5 MeV/c2 (c is the speed of light) and e2/(4$$\pi$$$${{\varepsilon _0}}$$) = 1.44 MeV fm. Assuming that the difference between the binding energies of $$_7^{15}N$$ and $$_8^{15}O$$ is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10$$-$$15 m)
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 line of molybdenum (atomic number 42), then the ratio $$\lambda$$Cu/$$\lambda$$Mo is close to
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 answer using the codes given below the lists :
| List I | List II | ||
|---|---|---|---|
| P. | Alpha decay | 1. | $$_8^{15}O \to _7^{15}N + ...$$ |
| Q. | $${\beta ^ + }$$ decay | 2. | $$_{91}^{238}U \to _{90}^{234}Th + ...$$ |
| R. | Fission | 3. | $$_{83}^{185}Bi \to _{82}^{184}Pb + ...$$ |
| S. | Proton emission | 4. | $$_{94}^{239}Pu \to _{57}^{140}La + ...$$ |
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 electron?
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 line in the Balmer series of singly-ionized helium atom is
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 $${4 \over \pi } \times {10^{11}}$$ Hz. Then, the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2$$\pi$$ $$\times$$ 10$$-$$34 J-s)
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 the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of 4 $$\times$$ 10$$^{-15}$$ m is in the range
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 Lawson criterion?
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 half lives of S1 and S2 can be :
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