Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
The Nucleus

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Nucleus

Suppose that the mass of a nucleus is roughly given by M = A m_p ,...

Suppose that the mass of a nucleus is roughly given by M=AmpM = A m_p, where AA represents the mass number. Estimate the density of matter inside a nucleus in kg m−3\text{kg m}^{-3}, and determine the specific gravity of nuclear matter.

Options

  1. A3×1017 kg m−33 \times 10^{17} \text{ kg m}^{-3} and 3×10173 \times 10^{17}
  2. B3×1017 kg m−33 \times 10^{17} \text{ kg m}^{-3} and 3×10143 \times 10^{14}
  3. C3×1014 kg m−33 \times 10^{14} \text{ kg m}^{-3} and 3×10113 \times 10^{11}
  4. D3×1014 kg m−33 \times 10^{14} \text{ kg m}^{-3} and 3×10173 \times 10^{17}

Correct answer

B. 3×1017 kg m−33 \times 10^{17} \text{ kg m}^{-3} and 3×10143 \times 10^{14}

Step-by-step solution

The mass of the nucleus is given by M=AmpM = A m_p, where AA is the mass number and mp≈1.67×10−27 kgm_p \approx 1.67 \times 10^{-27} \text{ kg}.

The radius of the nucleus is R=R0A1/3R = R_0 A^{1/3}, where R0≈1.1×10−15 mR_0 \approx 1.1 \times 10^{-15} \text{ m}.

The volume of the nucleus is:

V=43πR3=43πR03AV = \dfrac{4}{3} \pi R^3 = \dfrac{4}{3} \pi R_0^3 A

The density of nuclear matter is:

ρ=MV=Amp43πR03A=mp43πR03\rho = \dfrac{M}{V} = \dfrac{A m_p}{\dfrac{4}{3} \pi R_0^3 A} = \dfrac{m_p}{\dfrac{4}{3} \pi R_0^3}

Substituting the standard values:

ρ=1.67×10−2743π(1.1×10−15)3≈3×1017 kg m−3\rho = \dfrac{1.67 \times 10^{-27}}{\dfrac{4}{3} \pi (1.1 \times 10^{-15})^3} \approx 3 \times 10^{17} \text{ kg m}^{-3}

The specific gravity is the ratio of the density of the nuclear matter to the density of water (ρw=103 kg m−3\rho_w = 10^3 \text{ kg m}^{-3}):

Specific gravity=ρρw=3×1017103=3×1014\text{Specific gravity} = \dfrac{\rho}{\rho_w} = \dfrac{3 \times 10^{17}}{10^3} = 3 \times 10^{14}
Practice The Nucleus on Quantrex Academy →

More from The Nucleus

A neutron star possesses a density equivalent to that of nuclear matter. Assuming the… Concepts Of Physics MCQ Edition [Volume 2]Determine the amount of energy released during the reaction given below: ^ 7 Li + p → α +… Concepts Of Physics MCQ Edition [Volume 2]Determine the binding energy per nucleon of ^ 197 _ 79 Au , given that its atomic mass is… Concepts Of Physics MCQ Edition [Volume 2]Compute the energy released if an α -particle is emitted by ^ 238 U . The atomic masses… Concepts Of Physics MCQ Edition [Volume 2]Determine the mass of an α -particle, given that its binding energy is 28.2 MeV . Concepts Of Physics MCQ Edition [Volume 2]Compute the energy that needs to be supplied to ^ 238 U in order for two protons and two… Concepts Of Physics MCQ Edition [Volume 2]Calculate the energy released in the nuclear reaction ^ 223 Ra → ^ 209 Pb + ^ 14 C . The… Concepts Of Physics MCQ Edition [Volume 2]Evaluate the minimum energy required to separate a proton from a nucleus containing Z… Concepts Of Physics MCQ Edition [Volume 2] Full The Nucleus list All Concepts Of Physics MCQ Edition [Volume 2] PYQs