$\sqrt{d_{1}}$ and $\sqrt{d_{2}}$ are the impact parameters corresponding to scattering angles $60^{\circ}$ and $90^{\circ}$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For $d_{1}=x d_{2}$, the value of x will be ____.

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Modern Physics

d_{1}

and

d_{2}

are the impact parameters corresponding to scattering angles

6 0^{\circ}

and

9 0^{\circ}

respectively, when an

α

particle is approaching a gold nucleus. For

d_{1} = x d_{2}

, the value of x will be ____.

Answer: 3

Solution

In Rutherford scattering, the impact parameter

d

is related to the scattering angle

θ

by:

d \propto cot (\frac{θ}{2})

For

θ_{1} = 6 0^{\circ}

and

θ_{2} = 9 0^{\circ}

\frac{d _{1}}{d _{2}} = \frac{cot ^{2} ( 3 0 ^{\circ} )}{cot ^{2} ( 4 5 ^{\circ} )} = \frac{( 3 ) ^{2}}{1 ^{2}} = 3

Therefore,

x = 3

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Integer answer

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 →