Atomic Models & Alpha-Particle Scattering

In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot?

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because

A. The size of gold nucleus is very small as compared to the size of gold atom.

B. Alpha particle and gold nucleus have equal charge.

C. The impact parameter is minimum for a few alpha particles.

D. A few alpha particles have very high kinetic energy.

E. Only a few alpha particles undergo head-on collision with the nuclei.

Choose the correct answer from the options given below:

$7.9\text{ MeV }\alpha$-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.

$\Bigg[\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2$ and electron charge $= 1.6 \times 10^{-19}\text{ C}\Bigg]$

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m. (Atomic number of gold $= 79$ and $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ in SI units)

Given below are two statements:

Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges.

Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below.

Given below are two statements:

Statement I: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

Statement II: An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the options given below

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5 \times 10^{-14}\text{ m}$. If target nucleus has atomic number 80, then maximum velocity of $\alpha$-particle is __________ $\times 10^{5}\text{ m/s}$ approximately.

( $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ SI}$ unit, mass of $\alpha$ particle $= 6.72 \times 10^{-27}\text{ kg}$)

Choose the correct option from the following options given below:

A nuclear physicist performed an experiment on the scattering of alpha particles by thin metal foil of gold. The alpha particles were accelerated up to kinetic energy 3.2 Mev. The estimation of the radius of the nucleus of gold element ($Z = 79$) by him is _______ $\times 10^{-16}\text{ m}$

(Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\ \frac{\text{N m}^2}{\text{C}^2}$)

$\sqrt{d_1}$ 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 d1 = x d2, the value of x will be ____________.

The graph which depicts the results of Rutherford gold foil experiment with $\alpha$-particales is: $\theta$: Scattering angle

Y: Number of scattered $\alpha$-particles detected (Plots are schematic and not to scale)

When an $\alpha$-particle of mass m moving with velocity v bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as

An alpha nucleus of energy $\frac{1}{2}$ mv2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

In a Rutherford scattering experiment when a projectile of charge z1 and mass M1 approaches a target nucleus of charge z2 and mass M2, the distance of closest approach is r0. The energy of the projectile is

An alpha nucleus of energy $\frac{1}{2}mv^2$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to

An $\alpha$-particle of energy $5\text{ MeV}$ is scattered through $180^\circ$ by a fixed uranium nucleus. The distance of closest approach is of the order of