A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is:
- 1:1
- 4:5
- 5:4
- 25:16:00
The Correct Option is C
Solution and Explanation
To determine the ratio of the radii of the two daughter nuclei, we use the formula for the nuclear radius: \( R = R_0 \cdot A^{1/3} \), where \( R_0 \) is a constant and \( A \) is the mass number.
Let the mass numbers of the daughter nuclei be \( A_1 = 125 \) and \( A_2 = 64 \).
The radius of the first nucleus \( R_1 \) is given by \( R_1 = R_0 \cdot 125^{1/3} \).
The radius of the second nucleus \( R_2 \) is given by \( R_2 = R_0 \cdot 64^{1/3} \).
We need the ratio \( \frac{R_1}{R_2} \), which is \(\frac{R_0 \cdot 125^{1/3}}{R_0 \cdot 64^{1/3}}\).
The \( R_0 \) terms cancel out, simplifying to \(\frac{125^{1/3}}{64^{1/3}}\).
This further simplifies to \(\left(\frac{125}{64}\right)^{1/3}\).
\( \frac{125}{64} = \frac{5^3}{4^3} \).
Thus, \(\left(\frac{5^3}{4^3}\right)^{1/3} = \frac{5}{4}\).
The ratio of the radii of the two daughter nuclei is \( 5:4 \).
Top Questions on Nuclear physics
- (a) Consider the so-called ‘D-T reaction’ (Deuterium-Tritium reaction).
In a thermonuclear fusion reactor, the following nuclear reaction occurs: \[ \ ^{2}_1 \text{H} + \ ^{3}_1 \text{H} \longrightarrow \ ^{4}_2 \text{He} + \ ^{1}_0 \text{n} + Q \] Find the amount of energy released in the reaction.
% Given data Given:
\( m\left(^{2}_1 \text{H}\right) = 2.014102 \, \text{u} \)
\( m\left(^{3}_1 \text{H}\right) = 3.016049 \, \text{u} \)
\( m\left(^{4}_2 \text{He}\right) = 4.002603 \, \text{u} \)
\( m\left(^{1}_0 \text{n}\right) = 1.008665 \, \text{u} \)
\( 1 \, \text{u} = 931 \, \text{MeV}/c^2 \)- CBSE CLASS XII - 2025
- Physics
- Nuclear physics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The density of the copper ($^{64}Cu$) nucleus is greater than that of the carbon ($^{12}C$) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.
In the light of the above statements, choose the most appropriate answer from the options given below:- JEE Main - 2025
- Physics
- Nuclear physics
- If an electron in the excited state falls to ground state, a photon of energy 5 eV is emitted, then the wavelength of the photon is nearly
- AP EAPCET - 2025
- Physics
- Nuclear physics
Match the LIST-I with LIST-II
LIST-I (Type of decay in Radioactivity) LIST-II (Reason for stability) A. Alpha decay III. Nucleus is mostly heavier than Pb (Z=82) B. Beta negative decay IV. Nucleus has too many neutrons relative to the number of protons C. Gamma decay I. Nucleus has excess energy in an excited state D. Positron Emission II. Nucleus has too many protons relative to the number of neutrons
Choose the correct answer from the options given below:- CUET (PG) - 2025
- Physics
- Nuclear physics
- Half life of a radioactive material during radioactive decay is \(\underline{\hspace{1cm}}\).
- CUET (PG) - 2025
- Atmospheric Science
- Nuclear physics
Questions Asked in NEET exam
The output (Y) of the given logic implementation is similar to the output of an/a …………. gate.
- NEET (UG) - 2025
- Logic gates
- Two identical point masses P and Q, suspended from two separate massless springs of spring constants \(k_1\) and \(k_2\), respectively, oscillate vertically. If their maximum velocities are the same, the ratio of the amplitude of P to the amplitude of Q is :
- NEET (UG) - 2025
- Waves and Oscillations
- A particle of mass \(m\) is moving around the origin with a constant speed \(v\) along a circular path of radius \(R\). When the particle is at \( (0, R) \), its velocity is \( \mathbf{v} = -v \hat{\mathbf{i}} \). The angular momentum of the particle with respect to the origin is :
- NEET (UG) - 2025
- The Angular Momentum
- The radius of Martian orbit around the Sun is about 1.5 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?
- NEET (UG) - 2025
- Kepler’s laws
- A balloon is made of a material of surface tension S and has a small outlet. It is filled with air of density \( \rho \). Initially the balloon is a sphere of radius R. When the gas is allowed to flow out slowly at a constant rate, its radius shrinks as \( r(t) \). Assume that the pressure inside the balloon is \( P(r) \) and is more than the outside pressure (\( P_0 \)) by an amount proportional to the surface tension and inversely proportional to the radius. The balloon bursts when its radius reaches \( r_0 \). Then the speed of gas coming out of the balloon at \( r = R \) is :
- NEET (UG) - 2025
- Surface Tension
Concepts Used:
Nuclear Physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons
Radius of Nucleus
‘R’ represents the radius of the nucleus. R = RoA1/3
Where,
- Ro is the proportionality constant
- A is the mass number of the element
Total Number of Protons and Neutrons in a Nucleus
The mass number (A), also known as the nucleon number, is the total number of neutrons and protons in a nucleus.
A = Z + N
Where, N is the neutron number, A is the mass number, Z is the proton number
Mass Defect
Mass defect is the difference between the sum of masses of the nucleons (neutrons + protons) constituting a nucleus and the rest mass of the nucleus and is given as:
Δm = Zmp + (A - Z) mn - M
Where Z = atomic number, A = mass number, mp = mass of 1 proton, mn = mass of 1 neutron and M = mass of nucleus.