JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Modern Physics

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

(A) $A^{3}$
(B) $A^{\frac{1}{3}}$
(C) $A^{\frac{2}{3}}$
(D)Independent of A✓ Correct

Answer: (D)

Solution

The nuclear radius follows

R = R_{0} A^{1/3}

, so the volume

\frac{4}{3} π R^{3} = \frac{4}{3} π R_{0}^{3} A

grows in direct proportion to

A

. The mass is close to

A

times the nucleon mass, so in the density

ρ = \frac{A m _{u}}{\frac{4}{3} π R _{0}^{3} A} = \frac{3 m _{u}}{4 π R _{0}^{3}}

the mass number cancels. The mass density of a nucleus is independent of

A

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Modern Physics →

More JEE Main questions on Modern Physics

7.9 MeV α-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.
[ $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}$ Nm²/C² and electron charge $= 1.6 \times 1 0^{- 19}$ C]
JEE Main 2026View solution →
The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 α$ particles is ______ kHz.
[mass of He nucleus = 4.002 amu, $1$ amu $= 1.66 \times 1 0^{- 27}$ kg, $h = 6.6 \times 1 0^{- 34}$ J.s and $c = 3 \times 1 0^{8}$ m/s]
JEE Main 2026View solution →
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly $____$ nm.
JEE Main 2026View solution →
Light is incident on a metallic plate having work function $110 \times 1 0^{- 20} J$ . If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ $rad / s$ . ( …
JEE Main 2026View solution →
The energy of an electron in an orbit of the Bohr's atom is $- 0.04 E_{0} eV$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then …
JEE Main 2026View solution →
A particle having electric charge $3 \times 1 0^{- 19} C$ and mass $6 \times 1 0^{- 27} kg$ is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is $α \times 1 0^{- 12} m$ . The va …
JEE Main 2026View solution →