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A radioactive material decays by simultaneous emission of two particles with respective half lives 1620 and 810 years. The time in years, after which one fourth of the material remains is
  • a)
    4860
  • b)
    2340
  • c)
    1080.0
  • d)
    3240
Correct answer is option 'C'. Can you explain this answer?

Nikita Singh answered
Since, from Rutherford-Soddy law, the number of atoms left after half-lives is given by
N=N0​(1/2​)n
where, N0​ is the original number of atoms.
The number of half-lives, n= time of decay​/effective half−life
Relation between effective disintegration constant (λ) and half-life (T)
λ=ln2/T​
∴λ1​+λ2​= (​ln2/ T1​)+ ​(ln2/ T2​)
Effective half-life,
1/T​=1/T1​​+1/T2​​=(1/1620)​+(1/810)​
1/T​=1+2/1620 ​⇒T=540yr
∴n=T/540
∴N=N0​(1/2​)t/540⇒N/N0​​=(1/2​)2=(1/2​)t/540
⇒t/540​=2⇒t=2×540=1080yr

All nuclides with same mass number A are called
  • a)
    isobars
  • b)
    isoclines
  • c)
    isotones
  • d)
    isotopes
Correct answer is option 'A'. Can you explain this answer?

Rocky Handsome answered
Isobars are atoms of different elements with the same mass number but different atomic numbers.

• Isotones are atomic nuclei with the same number of neutrons (N) and different number of protons(Z)

90% of a radioactive sample is left undisintegrated after time τ has elapsed, what percentage of initial sample will decay in a total time2τ?
  • a)
    9%
  • b)
    38%
  • c)
    19%
  • d)
    62%
Correct answer is option 'C'. Can you explain this answer?

Krishna Iyer answered
Given that 90% is left un-decayed after time 't'.
Hence, 10% decays in time 't'.
Initially assume that the amount of substance is 'x'
After time 't' 10% is decayed.
i.e. Amount of substance left =0.9x
After further time 't' another 10% is decayed.
i.e. 0.1×0.9x is decayed 
Leaving behind 0.81x.
Hence after time 2t we see that 0.19x has decayed, which is 19%.
 

α-rays are
  • a)
    helium nuclei
  • b)
    heavy nuclei
  • c)
    lithium nuclei
  • d)
    hydrogen nuclei
Correct answer is option 'A'. Can you explain this answer?

Ræjû Bhæï answered
Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways.

Nuclear mass M is found to be
  • a)
    always greater than total mass of its individual protons and neutrons
  • b)
    always equal to the total mass of its individual neutrons
  • c)
    always equal to the total mass of its individual protons and neutrons
  • d)
    always less than total mass of its individual protons and neutrons
Correct answer is option 'D'. Can you explain this answer?

Ritu Singh answered
The actual mass is always less than the sum of the individual masses of the constituent protons and neutrons because energy is removed when the nucleus is formed. This energy has mass, which is removed from the total mass of the original particles.

The average number of neutrons released by the fission of one uranium atom is
a)3.0
b)2
c)2.5
d)1
Correct answer is option 'C'. Can you explain this answer?

Bhanu Saini answered
Fission result in the production of typically 2 or 3 neutron so on the average about 2.5 neutron released per unit. so correct answer is option a
for option c one uranium atom split into one barium and one krypton atom releasing 3 neutron.
but in this question average is asking so according to me and books 2.5 is correct

What percentage of the mass of an atom is concentrated in the nucleus?
  • a)
    79.9%
  • b)
    99.9%
  • c)
    66.9%
  • d)
    50.9%
Correct answer is option 'B'. Can you explain this answer?

Jyoti Kapoor answered
More than 99.99% of the mass of any atom is concentrated in its nucleus. If the mass of protons and neutrons (which are in the nucleus of every atom) is approximately one (1) atomic mass unit, then the relative mass of an electron is 0.0005 atomic mass units.

Plutonium decays with a half-life of 24000 years. If the plutonium is stored for 72000 years, then the fraction of plutonium that remains is    
  • a)
    1 /3
  • b)
    1 /2
  • c)
    1/8
  • d)
    1 /4
Correct answer is option 'C'. Can you explain this answer?

Mira Sharma answered
The amount of plotinium after a time period of 72000 if the half life is 24000 will be 

the initial amount x would be reduced to x/2 , in 24000 yrs 

then it would lessen to x/4 in the next 24000yrs 

and then to x/8 in the next 24000 yrs 

that is it will reduce to x/8 in the next 72000yrs starting from x . 

In the mass number range A = 30 to 170, the binding energy per nucleon is
  • a)
    decreases with increasing A
  • b)
    increases linearly with A
  • c)
    decreases linearly with A
  • d)
    nearly constant
Correct answer is option 'D'. Can you explain this answer?

Binding energy per nucleon in the mass number range A = 30 to 170

The binding energy per nucleon is the energy required to separate a nucleus into its constituent nucleons. It is a measure of the stability of the nucleus, and it depends on the mass number of the nucleus. In the mass number range A = 30 to 170, the binding energy per nucleon is nearly constant. This means that the stability of the nucleus is nearly constant in this range.

Explanation:

The binding energy per nucleon is given by the formula:

BE/A = (ZmH + NmN - M)/A

where BE is the binding energy, Z is the atomic number, N is the number of neutrons, mH is the mass of a hydrogen atom, mN is the mass of a neutron, and M is the mass of the nucleus.

In the mass number range A = 30 to 170, the binding energy per nucleon is nearly constant because the nuclear force between nucleons is nearly constant. This means that the energy required to separate a nucleon from the nucleus is nearly constant in this range.

The nuclear force between nucleons is a strong force that holds the nucleus together. It is a short-range force that depends on the distance between nucleons. In the mass number range A = 30 to 170, the distance between nucleons is nearly constant, and so the nuclear force is nearly constant.

Therefore, the binding energy per nucleon is nearly constant in this range because the nuclear force is nearly constant. This means that the stability of the nucleus is nearly constant in this range.

In what units is mass measured on the atomic scale?
  • a)
    kilogram
  • b)
    atomic mass units (u)
  • c)
    milligram
  • d)
    gram
Correct answer is option 'B'. Can you explain this answer?

Lavanya Menon answered
The atomic mass of an element is the average mass of the atoms of an element measured in atomic mass unit (amu, also known as daltons, D). The atomic mass is a weighted average of all of the isotopes of that element, in which the mass of each isotope is multiplied by the abundance of that particular isotope.

The nuclei of isotopes of a given element contain the same number of
  • a)
    neutrinos
  • b)
    protons
  • c)
    neutrons
  • d)
    positrons
Correct answer is option 'B'. Can you explain this answer?

Atom of same element, contain same number of protons, they differ in number of neutrons .
This is known as isotope .
Therefore we can conclude that answer is [ B ]

Nuclear fusion is possible
  • a)
    only between light nuclei
  • b)
    only between heavy nuclei
  • c)
    between both light and heavy nuclei
  • d)
    only between nuclei which are stable against β-decay
Correct answer is option 'A'. Can you explain this answer?

In nuclear fusion, two or more small nuclei combine to form a single larger nucleus, a neutron, and a tremendous amount of energy. Nuclear fusion of hydrogen to form helium occurs naturally in the sun and other stars. It takes place only at extremely high temperatures.

B210has a half life of 5 days. The time taken for seven-eighth of a sample to decay is
  • a)
    10 days
  • b)
    20 days
  • c)
    3.4 days
  • d)
    15 days
Correct answer is option 'D'. Can you explain this answer?

Srishti Chavan answered
Half-life of Bi210=5 days
∴k= 0.693/(t1/2) ​=(0.693/5) ​day−1
Using k=(2.303/t)​ log (a/a-x)
(where a = a0​, (let) ⇒x=7/8 ​a0​, t is time taken in decay and k is rate constant)
We get, t=(2.303×5/0.693)log a0​/(1/8)a0​​
= (2.303×5/0.693) ​log8=15days
 

Choose the WRONG statement. A thermonuclear fusion reactor is better than a fission reactor for the following reason:
  • a)
    For the same mass of substances involved, a fusion reaction releases much more energy than a fission reaction.
  • b)
    The fuel required for fusion is readily available in abundance from seawater.
  • c)
    A fusion reaction can be much more easily controlled than a fission
  • d)
    A fusion reaction produces almost no radioactive waste.
Correct answer is option 'B'. Can you explain this answer?

Nisha Kulkarni answered
Explanation:
The wrong statement among the given options is option B: "The fuel required for fusion is readily available in abundance from seawater."

Reason:
- While it is correct that a thermonuclear fusion reactor is better than a fission reactor for several reasons, including higher energy release and less radioactive waste production, the availability of fuel from seawater is not accurate.
- Fusion reactions require isotopes of hydrogen, such as deuterium and tritium, as fuel. Deuterium can be extracted from seawater, but tritium is a radioactive isotope that is not naturally abundant and needs to be produced artificially.
- Tritium can be produced by exposing lithium to neutron radiation, which can be generated by a fission reactor or a fusion reactor itself. However, the process of producing tritium is not as straightforward as extracting deuterium from seawater.
- Tritium is also highly radioactive and has a short half-life, which means it requires careful handling and containment. It cannot be easily stored or transported.
- Therefore, the fuel required for fusion reactions is not readily available in abundance from seawater, as stated in option B.

Correct statements:
a) For the same mass of substances involved, a fusion reaction releases much more energy than a fission reaction.
- This is true. Fusion reactions release a tremendous amount of energy, several times more than fission reactions. The fusion of hydrogen atoms into helium is the same process occurring in the Sun and other stars, which produces immense amounts of energy.

c) A fusion reaction can be much more easily controlled than a fission reaction.
- This is true. Fusion reactions require extremely high temperatures and pressures to sustain, and if these conditions are not maintained, the reaction will cease. This inherent stability makes fusion reactions more easily controllable than fission reactions, which can lead to runaway chain reactions if not properly regulated.

d) A fusion reaction produces almost no radioactive waste.
- This is true. Fusion reactions do not produce long-lived radioactive waste like fission reactions. The only radioactive byproduct of fusion is tritium, which has a relatively short half-life and can be managed safely.

In summary, option B is the wrong statement because the fuel required for fusion reactions is not readily available in abundance from seawater.

Which of the following particles can be added to the nucleus of an atom without changing its chemical properties?
  • a)
    Alpha Particles
  • b)
    Protons
  • c)
    Neutrons
  • d)
    Electrons
Correct answer is option 'C'. Can you explain this answer?

Rajat Kapoor answered
Adding a neutron to the nucleus will make no change in the chemical properties of the atom. The atom will have the same number of protons and therefore the same number of electrons. It is the number of electrons that determines chemical properties.

Actually, with hydrogen the addition of a neutron will almost double its mass and thus cause it to behave a little differently chemically.

Of course if the added neutron causes the nucleus to fission, decay, or otherwise change, that will change the chemistry.

When a hydrogen bomb explodes, which of the following is used?
  • a)
    fission
  • b)
    both
  • c)
    neither of two
  • d)
    fusion
Correct answer is option 'B'. Can you explain this answer?

Naina Bansal answered
Hydrogen bomb or H-bomb, weapon deriving a large portion of its energy from the nuclear fusion of hydrogen isotopes. In an atomic bomb, uranium or plutonium is split into lighter elements that together weigh less than the original atoms, the remainder of the mass appearing as energy. Unlike this fission bomb, the hydrogen bomb functions by the fusion, or joining together, of lighter elements into heavier elements. The end product again weighs less than its components, the difference once more appearing as energy. Because extremely high temperatures are required in order to initiate fusion reactions, the hydrogen bomb is also known as a thermonuclear bomb. 

When a hydrogen bomb explodes, which of the following is used?
  • a)
    fission
  • b)
    fusion
  • c)
    neither of two
  • d)
    both
Correct answer is option 'D'. Can you explain this answer?

Dr Manju Sen answered
The hydrogen bomb is a nuclear weapon that uses a mixture of fission and fusion to produce a massive explosion.
The nuclear fission generates enough heat to initiate the nuclear fusion reaction. After that, the nuclear fusion releases enormous amounts of energy, making the hydrogen bomb a lot more powerful than an atomic bomb.

Nuclear forces are
  • a)
    spin dependent and have no non-central part
  • b)
    spin dependent and have a non-central part
  • c)
    spin independent and have no non-central part
  • d)
    spin independent and have a non-central part
Correct answer is option 'D'. Can you explain this answer?

EduRev JEE answered
Nuclear forces are fundamental interactions that govern the behaviour of protons and neutrons within an atomic nucleus. Here are some key characteristics:
  • The nuclear force is spin independent, meaning it does not rely on the spin orientation of nucleons.
  • It has a non-central part, which implies that the force varies with the spatial arrangement of nucleons.
  • This force is significantly stronger than the Coulomb force, which acts between charged particles.
  • The nuclear force operates over a very short range, typically around a few femtometres (fm).
In summary, the nuclear force is essential for holding the nucleus together, overcoming the repulsive forces between positively charged protons, and ensuring the stability of atomic nuclei.

Energies associated with nuclear processes are
  • a)
    about a 100 times larger than chemical process
  • b)
    about a million times larger than chemical process
  • c)
    about a thousand times larger than chemical process
  • d)
    about a ten times larger than chemical process
Correct answer is option 'B'. Can you explain this answer?

Unlike a chemical reaction, a nuclear reaction results in a significant change in mass and an associated change of energy, as described by Einstein’s equation. Nuclear reactions are accompanied by large changes in energy, which result in detectable changes in mass. The change in mass is related to the change in energy according to Einstein’s equation: ΔE = (Δm)c2. Large changes in energy are usually reported in kiloelectronvolts or megaelectronvolts (thousands or millions of electronvolts). With the exception of 1H, the experimentally determined mass of an atom is always less than the sum of the masses of the component particles (protons, neutrons, and electrons) by an amount called the mass defect of the nucleus. The energy corresponding to the mass defect is the nuclear binding energy, the amount of energy released when a nucleus forms from its component particles. In nuclear fission, nuclei split into lighter nuclei with an accompanying release of multiple neutrons and large amounts of energy. The critical mass is the minimum mass required to support a self-sustaining nuclear chain reaction. Nuclear fusion is a process in which two light nuclei combine to produce a heavier nucleus plus a great deal of energy.

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