Mass numbers of two nuclei are in the ratio of \(4 : 3\). Their nuclear densities will be in the ratio of
- \(4 : 3\)
- \(\bigg(\frac{3}{4}\bigg)^{\frac{1}{3}}\)
- \(1:1\)
- \(\bigg(\frac{4}{3}\bigg)^{\frac{1}{3}}\)
The Correct Option is C
Solution and Explanation
\(R = R_0A^{\frac{1}{3}}\)
\(⇒ \frac{R_1}{R_2} = \bigg(\frac{A_1}{A_2}\bigg)^\frac{1}{3}\)
\(= \bigg(\frac{4}{3}\bigg)^{\frac{1}{3}}\)
Ratio of density between two nuclei: \(\frac{ρ_1}{ρ_2} = \frac{\frac{A_1}{V_1}}{\frac{A_2}{V_2}}\)
= \(\bigg(\frac{A_1}{A_2}\bigg) \times \bigg(\frac{R_2}{R_1}\bigg)^3\)
= \(1 : 1\)
Top Questions on Nuclei
- If the radius of the first Bohr orbit is \( r \), then the radius of the second Bohr orbit will be
- The mass defect in a particular reaction is \( 0.4 \, \text{g} \). The amount of energy liberated is \( n \times 10^7 \, \text{kWh} \), where \( n = \) _____. (speed of light \( = 3 \times 10^8 \, \text{m/s} \))
- The half-lives of two radioactive materials A and B are respectively \( T \) and \( 2T \). If the ratio of the initial masses of the materials A and B is 8:1, then the time after which the ratio of the masses of the materials A and B becomes 4:1 is:
- The disintegration energy \( Q \) for the nuclear fission of \( ^{235}\text{U} \to ^{140}\text{Ce} + ^{94}\text{Zr} + n \) is _____ MeV.
Given atomic masses:
\[^{235}\text{U} = 235.0439 \, u, \quad ^{140}\text{Ce} = 139.9054 \, u, \quad ^{94}\text{Zr} = 93.9063 \, u, \quad n = 1.0086 \, u\]Value of \( c^2 = 931 \, \text{MeV/u} \). - In a radioactive sample \( 2 \times 10^8 \) nuclei reduce to \( 10^8 \) nuclei in 15 minutes, then the half-life of the sample in minutes is:
Questions Asked in JEE Main exam
The remainder when \( 64^{64} \) is divided by 7 is equal to:
- JEE Main - 2025
- Arithmetic Progression
- The sum of the infinite series $ \cot^{-1} \left( \frac{7}{4} \right) + \cot^{-1} \left( \frac{19}{4} \right) + \cot^{-1} \left( \frac{39}{4} \right) + \cot^{-1} \left( \frac{67}{4} \right) + ... $ is:
- JEE Main - 2025
- Sequence and series
- If $ \alpha $ is a root of the equation $ x^2 + x + 1 = 0 $ and $$ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20$$, then n is equal to _______
- JEE Main - 2025
- Sequence and series
x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)
- JEE Main - 2025
- Equilibrium
- The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
Concepts Used:
Nuclei
In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.
Read More: Nuclei
Following are the terms related to nucleus:
- Atomic Number
- Mass Number
- Nuclear Size
- Nuclear Density
- Atomic Mass Unit