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The correct option is (a) 1

The EXPLANATION is: For a nuclear reactor, k = 1. It is the RATIO of the number of neutrons produced in a nuclear pile to the number DISAPPEARING that must equal to UNITY for a chain reaction.

Correct choice is (b) Q VALUE

Easy explanation: In a nuclear reaction, the sum of masses before the reaction is greater than the sum of masses after the reaction. The difference in masses appears in the form of energy following the law of inter-conversion of MASS and energy. Thus, the energy RELEASED in a nuclear reaction is called a Q value of a reaction.

Right option is (c) The nuclear force is independent of charge

To EXPLAIN: Nuclear force is independent of charge.The nuclear force between TWO protons is the same as that between two neutrons or between a neutron and PROTON. This is known as charge independent character of nuclear force. ALSO, nuclear force is stronger than the electromagnetic and gravitational force.

The correct OPTION is (a) Cadmium

The explanation is: In nuclear reactors, cadmium RODS are used as control rods. They are used to absorb the extra nucleons and to absorb neutrons, making them UNAVAILABLE to cause fission. The other OPTIONS are not VALID.

The correct option is (d) Barium

For explanation I would SAY: The breaking of a HEAVY nucleus into two or more fragments of comparable masses, with the release of a tremendous amount of energy is called nuclear fission. The most typical fission reaction occurs when slow-moving neutrons strike Uranium 235 to form the main product barium. The nuclear reaction is GIVEN as:

\( _{92}^{235}\)U + \(_0^1\)n ➔ \( _{56}^{141}\)Ba + \( _{36}^{92}\)KR + 3\( _{0}^{1}\)n + 200 MeV

Right option is (c) The decay of a neutron in nuclei

The BEST I can explain: In β-emission, a neutron of nucleus decays into a PROTON and a β-particle.

The REACTION GIVEN as:

0n^1 ➔ 1H^2 + -1e^0.

Correct option is (b) TWO places

Explanation: When a radioactive SUBSTANCE emits an α-particle, its ATOMIC number decreases by a factor of 2. Therefore, its position in the periodic table is ALSO LOWERED by two places.

Right choice is (b) False

Easy explanation: No, this is a false statement. Uncontrolled chain reactions form the basis of an atomic bomb. If the number of fissions in a given INTERVAL of time GOES on increasing CONTINUOUSLY, then a condition of an EXPLOSION is CREATED, and this is known as uncontrolled chain reactions.

The correct choice is (C) High temperature

The explanation is: TWO or more atomic nuclei are COMBINED to form one or more different atomic nuclei and subatomic particles. High temperature is essential for initiating the FUSION REACTION. The others are not an essential requirement.

Correct answer is (a) m ∝ V

Best explanation: MASS of NUCLEUS = Nuclear density × Volume.

The nuclear density of an atom is CONSTANT (10^-17 kgm^-3) for all nuclei, THEREFORE, the mass of the nucleus is directly proportional to the volume.

The correct ANSWER is (d) 27:1

To elaborate: Given: R1 = R0 (A1)^1/3 and R2 = R0 (A2)^1/3

\(\frac {R1}{R2} = (\frac {A1}{A2} ) ^{\frac {1}{3}} \) or \( \frac {A1}{A2} = (\frac {R1}{R2} )^3 = (\frac {1}{3} )^3 \)

\( \frac {A1}{A2} = \frac { 1}{27}\)

So, the ratio of their masses is given as:

\( \frac {m1}{m2} = \frac { 1}{27}\)

According to the principle of CONSERVATION of momentum, the magnitude of p1 = magnitude of p2

m1v1 = m2v2

\( \frac {V1}{v2} = \frac {m2}{m1} = \frac {27}{1}\) = 27:1.

Correct option is (c) More than half of the active NUCLEI decay

The best I can explain: In ONE AVERAGE life, i.e. at 7 hours, 63.2 % of the active nuclei will decay. Therefore, in a time of 7 hours, it can be CONSIDERED that more than half of the active nuclei will decay.

Right ANSWER is (d) Repulsion between the nuclei

Best explanation: For the fusion reaction to occur, the LIGHT nuclei are brought closer to each other, at a distance of about 10^-14 m. This is only possible at a very HIGH temperature to counter the repulsive force between the two nuclei. DUE to this reason, the fusion reaction is difficult to perform.

Correct CHOICE is (c) Controlled CHAIN reaction

The explanation is: In a chain reaction, the fast-moving neutrons are absorbed by certain substances KNOWN as moderators such as heavy water, then the NUMBER of fissions can be controlled and the chain reaction in such a case is known as a controlled chain reaction. This forms the BASIS of a nuclear reactor.

The CORRECT option is (a) 1080

The explanation: N = N0e^-(λ1 + λ2) t.

4 = e^(λ1 + λ2) t.

t = \(\frac {(2 \TIMES 1620 \times 810)}{(2430)}\) = 1080 year.

The CORRECT choice is (d) Heavy water

Explanation: Heavy water is used as a moderator in a NUCLEAR reactor. It slows down NEUTRONS and also has a low probability of absorption of neutrons. The other options are not VALID.

Correct option is (a) Fusion

Best EXPLANATION: At very high temperatures in the interior of the sun, protons fuse to form HELIUM nuclei, liberating a HUGE amount of energy. Therefore, the REACTION RESPONSIBLE for the production of light energy from the sun is fusion.

The CORRECT answer is (a) True

The best explanation: Yes, this is a true statement. An atom is SAID to be unstable, or in other words, radioactive when the FORCES that it is subjected to it are unbalanced. Therefore, when there is an EXCESS of internal energy, instability of an atom’s nucleus occurs and hence they can BECOME radioactive. This may also result from an excess of either neutrons or protons in the nucleus.

Correct choice is (c) Rutherford

The explanation: Rutherford was the form to measure the size of the nuclei of an atom by 1911. He discovered that these were about 10^4 TIMES smaller than the ATOMS that constituted them and this was due to the fascinating way that the alpha particles scattered from metal foils.

Right ANSWER is (d) 92U^235

Best EXPLANATION: The nucleus of Uranium 235(92U^235) has 234 – 92 = 142 neutrons.

Therefore, It has the highest PROTON to NEUTRON ratio, i.e.

= The NUMBER of protons: the number of neutrons

= 142:92

The correct answer is (a) BETA RAYS are the same as for cathode rays

Easiest explanation: β-rays are electrons of nuclear origin. Therefore, they have the same NATURE as the cathode rays. The other statements are not VALID.

Correct answer is (b) False

For explanation: No, this is a false STATEMENT. SOLAR ENERGY is mainly caused DUE to the fusion of PROTONS during the synthesis of heavier elements. So, it is not fission, but it is the fusion that results in solar energy.

Correct CHOICE is (B) False

For explanation I would say: No, this is a false statement. β-rays are charged particles emitted by RADIOACTIVE NUCLEI. THEREFORE, these rays are highly energetic electrons that are released from the inside of a nucleus. Thus, these are not electromagnetic radiations.

The correct answer is (c) \(\frac {5}{6}\)

BEST EXPLANATION: After one-half life, \(\frac {N_0}{2}\) sample remains and \(\frac {N_0}{2}\) decays.

After three half-lives, \(\frac {N_0}{6}\) sample remains and \(\frac {5N_0}{6}\) decays.

Hence the probability that a NUCLEUS undergoes decay after two half-lives is \(\frac {5}{6}\).

Correct answer is (a) True

For explanation I would say: Yes, this is a true statement. The nuclear force EXISTS in SMALL regions, i.e. the diameter of 10^-15 m = 1 fm. The nuclear force between TWO nucleons decreases rapidly as the separation between them increases and becomes NEGLIGIBLE at separation more than 10 fm.

Correct OPTION is (d) James Chadwick

For explanation I WOULD SAY: Neutrons are chargeless subatomic particles. It was discovered by James Chadwick in 1932. They are present in all-atom nuclei except those of ordinary hydrogen. The neutron was initially very difficult to DETECT and therefore, the last to be discovered.

The CORRECT OPTION is (C) 17.6 eV

To elaborate: 1H^2 + 1H^3 ➔ 2He^4 + 0n^1 + Q.

= [2.014 + 3.016 – 4.002 – 1.008] × 931.5 MeV.

= 17.6 MeV.

Right OPTION is (B) 20000 dps

Easy EXPLANATION: The EXPRESSION is given as:

R0 = 4R

4R = 4 × 5000

R0 = 20000dps.

The CORRECT ANSWER is (d) 2.31 min

Explanation: T1/2 = 0.693t

T1/2 = 0.693 × 200s

T1/2 = \(\FRAC {138.6}{60}\) min

T1/2 = 2.31 MINUTES

The CORRECT CHOICE is (b) Carbon

The best explanation: The REACTION is given as:

^22Ne10 ➔ 2 2He^4 + 6X^14.

Therefore, the unknown NUCLEUS is 6C^14.

Right choice is (d) Mass, energy, and momentum

Easy EXPLANATION: Two or more atomic nuclei are combined to form one or more DIFFERENT atomic nuclei and SUBATOMIC PARTICLES. In any nuclear REACTION, mass, energy, and momentum are conserved. So, all three are conserved.

Correct answer is (d) All have the same WAVELENGTH

The explanation: Wavelength of DE Broglie waves is GIVEN as:

λ = \(\frac {h}{p}\).

As momentum is the same for all RAYS, all have the same wavelength λ.

Correct option is (a) 60

To EXPLAIN: MAXIMUM number of electrons in an ORBIT = 2n^2.

As n > 4 is not allowed, the number of possible elements = 2(1)^2 + 2(2)^2 + 2(3)^2

Number of possible elements = 2(4)^2

Number of possible elements = 60.

Right option is (B) URANIUM-235

Explanation: A neutron, irrespective of whether it is slow or fast, can cause FISSION in a Uranium 235 nuclei. It absorbs a neutron and fissions into TWO new ATOMS by releasing some binding energy.

The correct ANSWER is (a) The attraction between protons and neutrons

Explanation: The protons and neutrons are HELD together by the strong attractive FORCES inside the nucleus of an ATOM. These forces are known as nuclear forces. The other statements are not valid and do not DEFINE nuclear forces.

Correct ANSWER is (a) μ ∝ N

To EXPLAIN: L = \(\frac {nh}{2\pi }\) and μ = \(\frac {eL}{2m}\).

μ = \(\frac {enh}{2m.2\pi }\)

Therefore, μ ∝ n.

The correct option is (a) Protons

For explanation: Protons are not emitted by RADIOACTIVE substances during their decay. They are POSITIVELY charged SUBATOMIC PARTICLES found in the atomic nucleus. The others can be emitted by radioactive substances during their decay.

Right option is (B) False

The best explanation: No, this is a false statement. The emission of β-rays can RESULT in CHANGES in the CHARGE of the nucleus but not the MASS of the nucleus. Mass of the nucleus is always conserved in radioactive decay.

Correct option is (b) The NUCLEUS with even number of protons and neutrons

For explanation: The nuclei of atoms having even NUMBERS of both protons and neutrons are the most stable ones and this ALSO means that they are less radioactive than NUCLIDES containing even numbers of protons and ODD numbers of neutrons.