Four statements are given (A is mass number) :
A. The volume of a nucleus is proportional to $A^{1/3}$.
B. The volume of a nucleus is proportional to A.
C. The difference in mass of an atom and its nucleus is called the mass defect.
D. The difference in mass of a nucleus and its constituent nucleons is called the mass defect.
Choose the correct answer from the options given below :
Nuclear Statement Analysis
We need to evaluate the truthfulness of four statements related to nuclear properties.
Statement A Analysis
The radius ($R$) of a nucleus is empirically found to be proportional to the cube root of the mass number ($A$): $R \propto A^{1/3}$
The volume ($V$) of a nucleus is proportional to the cube of its radius: $V \propto R^3$
Substituting the relation for $R$: $V \propto (A^{1/3})^3 = A$
Therefore, the volume of a nucleus is proportional to $A$, not $A^{1/3}$. Statement A is false.
Statement B Analysis
As derived above, the volume ($V$) of a nucleus is directly proportional to the mass number ($A$). $V \propto A$
Statement B is true.
Statement C Analysis
The mass defect is specifically defined as the difference between the mass of the individual nucleons (protons and neutrons) and the actual measured mass of the nucleus. The mass of electrons in an atom is generally not included in this specific definition of nuclear mass defect. Therefore, this statement is an inaccurate definition. Statement C is false.
Statement D Analysis
The mass defect ($\Delta m$) is precisely the difference between the total mass of the constituent nucleons (protons and neutrons) and the measured mass of the nucleus. $\Delta m = (\text{Mass of constituent nucleons}) - (\text{Mass of nucleus})$
Statement D provides the correct definition. Statement D is true.
Conclusion
Based on the analysis:
- Statement A is false.
- Statement B is true.
- Statement C is false.
- Statement D is true.
Therefore, statements B and D are true, while A and C are false.
Similar Questions
Match List I with List II :
List I List II A. $E = h\nu$ I. de Broglie wavelength B. Interference II. Particle nature of light C. $\lambda = h/p$ III. Wave nature of light D. Compton effect IV. Energy of photon
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(Take $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}, \text{ e} = 1.6 \times 10^{-19} \text{ C}$ and $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2$)- An unknown nucleus has a nuclear density of $2.29 \times 10^{17} \text{ kg/m}^3$ and mass of $19.926 \times 10^{-27} \text{ kg}$. Its mass number A is approximately :
(Take $R_0 = 1.2 \times 10^{-15} \text{ m}$, $4\pi = 12.56$) - A ray of light with wavelength $\lambda$ is incident on three different photo-electric cells namely 1, 2 and 3. The threshold wavelength of these photo-electric cells are $\lambda_1$, $\lambda_2$, and $\lambda_3$, respectively and the magnitude of stopping potentials of these cells are $V_1$, $V_2$ and $V_3$, respectively. The relation between $\lambda$ and threshold wavelengths are $\lambda_1 < \lambda$, $\lambda_2 > \lambda$ and $\lambda_3 \gg \lambda$. The correct option is :
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- Consider the following nuclear reaction :
$$^{238}\text{U} \rightarrow ^{234}\text{Th} + ^{4}\text{He}$$
Take masses of $^{238}\text{U}$, $^{234}\text{Th}$ and $^{4}\text{He}$ as $238.050\text{ u}$, $234.043\text{ u}$ and $4.003\text{ u}$, respectively. The Q value for the reaction, in keV, is :
[Given : $1\text{ u} = 931.5\text{ MeV c}^{-2}$] - A photon and an electron, each of $20\text{ eV}$ energy, move in free space. The ratio of linear momentum of electron $p_e$ to that of photon $p_{ph}$, $\frac{p_e}{p_{ph}}$ is :
(Take speed of light $= 3 \times 10^8\text{ ms}^{-1}$, charge of electron $= -1.6 \times 10^{-19}\text{ C}$ and mass of electron $= 9 \times 10^{-31}\text{ kg}$) - Consider that an electron is revolving in an excited state of Hydrogen atom with velocity $\sqrt{25.6} \times 10^5\text{ ms}^{-1}$. The radius of the orbit is $x \times 10^{-9}\text{ m}$. The value of $x$ is :
[Take the mass of electron to be $9 \times 10^{-31}\text{ kg}$, charge of electron $= 1.6 \times 10^{-19}\text{ C}$ and $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9\text{ N m}^2\text{ C}^{-2}$] - In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot ?
- A beam of light falls on a metal surface such that photo-electrons are generated. If power of the light source starts to decrease linearly with time $t$, then variation of the photocurrent $I$ and magnitude of the stopping potential $|V|$ with time is best represented by :
Important Questions from Modern Physics
Assuming in forward bias condition there is a voltage drop of $0.7 \text{ V}$ across a silicon diode, the current through diode $D_1$ in the circuit is ________$\text{mA}$.
(Assume all diodes in the given circuit are identical)
- The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n : 1$. The value of $n$ is ________.
(Assume mass of proton = mass of neutron) : - The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.
(R = Rydberg constant) - 7.9 MeV $\alpha$-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) _________ m.
$\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \text{ and electron charge} = 1.6 \times 10^{-19} \text{ C} \right]$ Find the correct combination of A, B, C and D inputs which can cause the LED to glow.
