Important Questions for Nuclei 

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Very Short Answer Questions (1 Mark Questions)

Ques. Define Atomic Number.

Ans. The number of protons which are present in the nucleus of an atom of the element is known as the atomic number of an element. It is also known as mass number. We can represent the mass number by the symbol “Z”.

Ques. What are Isotopes?

Ans. Isotopes are defined as nuclei which have the same number of neutrons but a different number of protons/atomic numbers. For example, Isotopes of hydrogen are Protium, Deuterium and Tritium.

Ques. Define the half-life of a radioactive element.

Ans. Half-life is the time in which the half number of atoms present initially in the sample decays. The relation derived between half-life and disintegration constant is represented by:

T = log2e / \(λ\) = 0.6931 / \(λ\)

Ques. What is Thermonuclear Energy?

Ans. Thermonuclear energy is the energy which is released during the process of nuclear fission. Protons are required in the process of fusion while neutrons are needed in the process of fission.

Ques. State Radioactive decay law. 

Ans. Radioactive decay law states the number of nuclei which are disintegrated of undecayed radioactive nuclei present at that instant. It can be written as:

N(t) = N(0) e-\(λ\)t

Where N(0) is the number of nuclei at t=0 and disintegration constant.

Ques. Define Mean life in brief.

Ans. The mean life of a radioactive sample is defined as the ratio of the combined age of all the atoms and the total number of atoms which are present in the given sample. It is given as:

T = T₁/2 / 0.693 = 1.44 T₁/2 

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Short Answer Questions (2 Marks Questions)

Ques. What are Nuclear Forces?

Ans. Nuclear forces are forces which are strong and attractive forces which hold protons and neutrons together in a tiny nucleus. These forces don't depend upon the charge of the nucleon. These are the forces which have a short-range and operate over a very short distance of about 2-3 fm of separation between any two nucleons.

Ques. Comment on the discovery of neutrons.

Ans. The discovery of neutrons was carried out by James Chadwick in 1932. When beryllium nuclei are bombarded by alpha-particles, highly penetrating radiations are emitted, which consist of neutral particles, each having a mass nearly that of the proton. These particles are known as neutrons. A free neutron decays spontaneously, with a half-life of about 900s, into a proton, electron and antineutrino.

Ques. Explain Radioactivity Displacement Law in brief.

Ans. Radioactivity Displacement Law states that -

• When a radioactive nucleus emits alpha-particles, the atomic number decreases by 2 and the mass number also decreases by 4.
• When a radioactive nucleus emits beta-particles, the atomic number increases by 1 and the mass number remains the same.
• When a radioactive nucleus emits gamma-particles, the atomic number and mass number remain the same. Its emission by the radioactive nucleus lowers its energy state.

Ques. Write down the name of the absorbing material required to control the reaction rate of neutrons during a reactor. List any two characteristic properties of nuclear force. 

Ans. The absorbing material required to control the reaction rate of neutrons during a reactor is the control rod or cadmium rod. Two properties of nuclear force are:

• They are the strongest forces in nature.
• They are charge independent.

Ques. (a) Explain that the mass of the nucleus in its ground state is always less than the total mass of its constituents - neutrons and protons.

(b) Plot a graph depicting the variation of the potential energy of a pair of nucleons as a function of their separation.

Ans. (a) When nucleons approach each other so as to form a nucleus, they attract each other. Their potential energy decreases and becomes negative. Potential energy holds the nucleons together in the nucleus. The decrease in potential energy causes a decrease in the mass of nucleons inside the nucleus. 

(b)  

Ques. Two nuclei have mass numbers in the ratio of 1:27. Calculate what will be the ratio of their nuclear radii?

Ans. As we know, 

R = R0 A^1/3

R1:R2 = (11/3: 27^1/3) = (1/27)^1/3 = 1:3

Ques. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6MeV is split into two fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5MeV per nucleon. Calculate what will be the energy Q released per fission in MeV. 

Ans. It is given that,

²⁴⁰X = ¹¹⁰Y + ¹³⁰Z

So, gain in binding energy for nucleon = 8.5 - 7.6 = 0.9MeV

Therefore, total gain in binding energy per nucleus fission = 240*0.9 = MeV

Ques. If both the number of protons and the number of neutrons are conserved in each nuclear reaction, then in what ways the mass is converted into energy (or vice-versa) in a nuclear reaction? Describe.

Ans. The sum of masses of nuclei of product elements is less than the sum of masses of reactants, hence loss of mass takes place during the reaction. This difference in mass of product element and reactant converts into energy and is released in the form of heat.

H²₁ + H²₁ -> H³₂ + n²₁ + energy

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Long Answer Questions (3 Marks Questions)

Ques. List down the limitations of J.J Thomson’s model of an atom. Define canal rays.

Ans. The model of J.J Thomson states that the mass of an atom is due to the presence of protons and electrons that are evenly spread throughout the atom which didn’t meet the observations made by Rutherford according to whom the mass is concentrated in a very small space. The results of the alpha particle scattering experiment couldn’t be explained by Thomson’s model.

The positively charged radiations which pass through the perforated cathode are known as canal rays. They contain particles which are positively charged and travel through another code in a gas discharge tube.

Thomson’s Atomic Model

Ques. If two nuclei have mass numbers in the ratio of 1:2. What will be the ratio of their nuclear densities?

Ans. Nuclear density (f) = Mass of nucleus / Volume of nucleus

But, R = R0A1/3

Now,

Where, m = mass of proton or neutron

A = no of nucleons

Hence, f is independent of mass number A.

Therefore, the ratio of density will be 1:1.

Ques. The half-life of a radioactive substance is given as X years. How long will it take the activity to reduce to 1% of its original value?

Ans. Let the amount of radioactive substance initially be N0

After the radioactive decay, the amount of radioactive substance is N

According to the question,

N/N0 = 1% = 1/100

N/N0 = e^\(-λt\)

e-λt = 1/100

-λt = ln1 - ln100

-λt = 0 - 4.0625

t = 4.0625/^\(λ\)

As, λ = 0.693/X

Then, t = 0.693/X = 6.645X

Therefore, the substance will take 6.645X years to reduce to 1% to the original value.

Ques. Explain why heavy water is used in moderators in a nuclear reactor?

Ans. In nuclear reactors, heavy water is used because it acts as a moderator in slowing down the neutrons which are produced during the fission reaction. This mainly helps in sustaining the chain reaction which allows nuclear reactors to operate efficiently and with stability. Uranium can be used as a reactor with heavy water used as a moderator in its natural state. Heavy water is also considered a good moderator as it can operate in high temperatures and has a low absorption probability for neutrons.

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Very Long Answer Questions (5 Marks Questions)

Ques. Calculate what will be the height of the potential barrier for a head-on collision of two deuterons. The height of the potential barrier is given by Coulomb's repulsion between the two deuterons when they just touch each other. Assume that hard spheres of radius 2.0 fm can be taken. 

Ans. In case when two deuterons collide head-on then, the distance between their centres will be: 

d = Radius of first deuteron + Radius of second deuteron

Radius of deuteron nucleus = 2fm = 2*10-15 m

d = 2*10-15 m + 2*10-15 m = 4*10-15 m

Charge on a deuteron nucleus = Charge on an electron = e = 1.6*10-19 C

Potential energy of two deuteron system, V = e2 / 4πε0d

where, ε0 refers to the permittivity of free space

1 / 4πε0 = 9*109 Mm2c-2

V = 9*10*(1.6*10-19)-2 / 4*10-15 J

V = 9*10*(1.6*10-19)-2 / 4*10-15 * (1.6*10-19) eV

V = 360 keV

Therefore, the height of the potential barrier of the two-deuteron system comes out to be 360 keV.

Ques. Difference between Isotopes and Isobars.

Ans. The difference between isotopes and isobars is as follows:

Ques. How is the size of the nucleus experimentally determined? Write the relation between the radius and mass number of the nucleus. Show that the density of the nucleus is independent of the mass number. 

Ans. The size of the nucleus is determined by the Rutherford experiment on alpha particle scattering. The distance of the nearest approach is approx the size of the nucleus. It is assumed that only coulomb repulsive force causes scattering. With alpha rays of 5.5 MeV, the size of the nucleus was less than 4*10-4 m. By doing scattering experiments with fast electrons bombarding targets of different elements, the size of the nuclei of various elements can be determined accurately.

The required relation is R = RoA1/3, where, Ro = 1.2*10-15 m

The density of nucleus of mass number A and radius R is given by:

Nuclear density = Mass of nucleus / Volume of nucleus

Nuclear density = A amu / 4/3πR3 

Nuclear density = A * 1.660565*10-27 / 4/3\(π\)R03 A

Nuclear density = 2.3*10-17 kgm-3 that is independent of the mass number A.

Ques. Give reasons for the following:

1. Why is the binding energy per nucleon found to be constant for nuclei in the range of mass numbers between 30 and 170?
2.  When a heavy nucleus with mass number A = 240 breaks up into two nuclei, A = 120 energy is released in the process.
3. In β-decay, the experimental detection of neutrinos is found to be extremely difficult.

Ans. The appropriate reasons for the following statements are as follows:

1. Nuclear forces are the forces which have short ranges. A particular nucleon inside a sufficiently large nucleus will be under the influence of some of its neighbours which come within the range of nuclear forces. The property that a given nucleon influences only nucleons close to it is referred to as the saturation property of nuclear force. That’s why the binding energy per nucleon was found to be constant for nuclei in the range of mass numbers between 30 and 170.
2. When a heavy nucleus with mass number A = 240 breaks up into two nuclei, A = 120 energy is released in the process. This is because the binding energy per nucleon of the parent nucleus is less than those of daughter nuclei. It is the increased binding energy which gets released in the process.
3. In β-decay, the experimental detection of neutrinos is found to be extremely difficult. This is because the neutrinos are chargeless and massless particles, and the interaction with other particles is almost negligible. Therefore, they can pass through very large quantities of matter without getting detected.

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