Q: M_n and M_p represent mass of neutron and proton respectively. If an element having atomic mass M has N-neutron and Z-proton, then the correct relation will be

M < [N M_n + Z M_p]. The actual atomic mass (M) of an element is slightly less than the sum of the masses of its neutrons and protons due to the mass defect, which accounts for the binding energy of the nucleus.

Q: A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size (nuclear radius)?

1 : 2^(1/3). The velocity ratio of the two parts is inversely proportional to the square root of their masses due to momentum conservation. Since nuclear radius is proportional to the cube root of mass, the ratio of radii will be the inverse cube root of the velocity ratio, i.e., 1 : 2^(1/3).

Question 1

Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be:

Accepted Answer

1:1. Nuclear density is independent of the mass number of a nucleus and remains constant for all nuclei. Hence, the ratio of their nuclear densities is 1:1.

Question 2

If radius of the 27/13 Al nucleus is taken to be R_Al, then the radius of 125/53 Te nucleus is nearly:

Accepted Answer

(53/13)^(1/3) R_Al. The radius of a nucleus is proportional to the cube root of its mass number (A). Thus, the ratio of the radii of two nuclei is proportional to the cube root of the ratio of their mass numbers. For 125/53 Te and 27/13 Al, the ratio is (53/13)^(1/3).

Question 3

If the nuclear radius of 27/13 Al is 3.6 Fermi, the approximate nuclear radius of 64/29 Cu in Fermi is:

Accepted Answer

4.8. The nuclear radius is proportional to the cube root of the mass number (A). Using the relation R ∝ A^(1/3), the ratio of radii is (R_Cu / R_Al) = (A_Cu / A_Al)^(1/3). Substituting A_Cu = 64 and A_Al = 27, we get R_Cu = 3.6 × (64/27)^(1/3) ≈ 4.8 Fermi.

Question 4

The radius of germanium (Ge) nuclide is measured to be twice the radius of 9/4 Be. The number of nucleons in Ge are:

Accepted Answer

74. The radius of a nucleus is proportional to the cube root of its mass number (A). If the radius of Ge is twice that of Be, then (A_Ge)^(1/3) = 2 × (A_Be)^(1/3). Solving for A_Ge using A_Be = 9 gives A_Ge = 74.

Question 5

If the nucleus 27/13 Al has nuclear radius of about 3.6 fm, then 125/32 Te would have its radius approximately as:

Accepted Answer

6.0 fm. The nuclear radius is proportional to the cube root of the mass number (A). Using the formula R = R₀A^(1/3), where R₀ is the proportionality constant, we calculate the radius of 125/32 Te relative to 27/13 Al. Since R₁/R₂ = (A₁/A₂)^(1/3), substituting A₁ = 125 and A₂ = 27 gives R₂ ≈ 6.0 fm.

Question 6

The nuclei of which one of the following pairs of nuclei are isobars?

Accepted Answer

54/26 Fe^(34), 31/15 Ga^(71). Isobars are nuclei with the same mass number but different atomic numbers. In option A, both nuclei have the same mass number (A = 71) but different atomic numbers (26 and 15), making them isobars.

Question 7

A nucleus represented by the symbol A/Z X has:

Accepted Answer

Z protons and (A-Z) neutrons. In the symbol A/Z X, Z represents the atomic number, which is the number of protons, and A represents the mass number, which is the total number of protons and neutrons. Therefore, the number of neutrons is (A-Z).

Question 8

The mass number of a nucleus is:

Accepted Answer

sometimes less than and sometimes more than its atomic number. The mass number of a nucleus is the sum of protons and neutrons, while the atomic number is the number of protons. Since neutrons can vary, the mass number can be greater than, equal to, or less than the atomic number depending on the isotope.

Question 9

M_n and M_p represent mass of neutron and proton respectively. If an element having atomic mass M has N-neutron and Z-proton, then the correct relation will be

Accepted Answer

M < [N M_n + Z M_p]. The actual atomic mass (M) of an element is slightly less than the sum of the masses of its neutrons and protons due to the mass defect, which accounts for the binding energy of the nucleus.

Question 10

A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size (nuclear radius)?

Accepted Answer

1 : 2^(1/3). The velocity ratio of the two parts is inversely proportional to the square root of their masses due to momentum conservation. Since nuclear radius is proportional to the cube root of mass, the ratio of radii will be the inverse cube root of the velocity ratio, i.e., 1 : 2^(1/3).

Question 11

The stable nucleus that has a radius half that of Fe^56 is

Accepted Answer

Li^7. The radius of a nucleus is proportional to the cube root of its mass number (A). Since the radius of the stable nucleus is half that of Fe^56, its mass number should be approximately (1/8) of 56, which is close to 7. Thus, the correct answer is Li^7.

Question 12

The mass number of He is 4 and that for sulphur is 32. The radius of sulphur nuclei is larger than that of helium by

Accepted Answer

√8. The nuclear radius is proportional to the cube root of the mass number (A). For helium, A = 4, and for sulfur, A = 32. The ratio of their radii is (32/4)^(1/3) = 2^(3/3) = √8.

Question 13

The nucleus which has radius one-third of the radius of Cs^189 is

Accepted Answer

^4_2He. The radius of a nucleus is proportional to the cube root of its mass number (R ∝ A^(1/3)). Since the radius of the desired nucleus is one-third of Cs^189, its mass number must be (1/3)^3 = 1/27 of 189, which is approximately 7. The closest option is ^4_2He.

Question 14

The mass number of a nucleus is equal to the number of

Accepted Answer

nucleons it contains. The mass number of a nucleus is defined as the total number of nucleons, which includes both protons and neutrons. Electrons are not part of the nucleus.

Question 15

The mass density of a nucleus varies with mass number A as

Accepted Answer

constant. The mass density of a nucleus is constant because the volume of the nucleus is proportional to the mass number A, and the mass is also proportional to A, leading to a constant density.

Question 16

The constituents of atomic nuclei are believed to be

Accepted Answer

neutrons and protons. Atomic nuclei are composed of neutrons and protons, collectively called nucleons. Electrons are not part of the nucleus.

Question 17

In the nucleus of ^23_11Na, the number of protons, neutrons and electrons are

Accepted Answer

11, 12, 0. The atomic number (11) represents the number of protons, and the mass number (23) minus the atomic number gives the number of neutrons (23 - 11 = 12). Electrons are not present in the nucleus.

Question 18

The nuclei ^13_6C and ^14_7N can be described as

Accepted Answer

isotones. Isotones are nuclei with the same number of neutrons. ^13_6C has 7 neutrons (13 - 6), and ^14_7N also has 7 neutrons (14 - 7), making them isotones.

Question 19

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

Accepted Answer

the helium nucleus has more kinetic energy than the thorium nucleus.. In nuclear decay, momentum is conserved. Since the helium nucleus is much lighter than the thorium nucleus, it must have a higher velocity to conserve momentum. Kinetic energy depends on both mass and velocity, and due to the helium nucleus's higher velocity, it will have more kinetic energy than the thorium nucleus.

Question 20

When a uranium isotope ^235_92U is bombarded with a neutron, it generates ^89_36Kr, three neutrons and:

Accepted Answer

^144_56Ba. The nuclear reaction must conserve both mass number and atomic number. The mass number of uranium (235) plus the neutron (1) equals 236. Subtracting the mass numbers of krypton (89) and three neutrons (3) leaves 144, which corresponds to barium. Similarly, the atomic number of uranium (92) minus krypton (36) and three neutrons (0) equals 56, which matches barium.

NEET Physics: Nuclei questions with solutions

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