Which of the following figure represents the variation of $\operatorname{ln}\left(\frac{\mathrm{R}}{\mathrm{R}_{0}}\right)$ with $\ln \mathrm{A}$ (If $\mathrm{R}=$ radius of a nucleus and $\mathrm{A}=$ its mass number)

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Modern Physics

Which of the following figure represents the variation of

ln (\frac{R}{R _{0}})

with

ln A

(If

R =

radius of a nucleus and

A =

its mass number)

(A)(see structure)
(B)(see structure)
✓ Correct
(C)(see structure)
(D)(see structure)

Answer: (B)

Solution

The nuclear radius is given by

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

. Taking natural logarithm:

ln R = ln R_{0} + \frac{1}{3} ln A

, which gives

ln (\frac{R}{R _{0}}) = \frac{1}{3} ln A

. This is a linear relation with slope

\frac{1}{3}

passing through the origin. The correct graph is option (B), showing a straight line with positive slope less than 1.

JEE Main · 2022 · 25 Jun 2022 · 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 →