In the study of Geiger-Marsdon experiment on scattering of $α - p a r t i c l e s$ by a this foil of gold, draw the trajectory of $α - p a r t i c l e s$ in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study:
From the relation $R = R_{0} A^{1 / 3}$ , where $R_{0}$ is constant and A is the mass number of the nucleus, show that nuclear matter density is independently of A

Open in App

Solution

The trajectory of $α$ - particles in the gold foil experiment is shown in the attached figure. As most of the particles are undeflected, this suggests that the nucleus occupies only a small volume of the total atom.

Let $m$ be the mass of the nucleon and $R$ be the radius of the nucleus.
Mass of the nucleus is $M = m A$
Volume of the nucleus is $V = \frac{4}{3} π R^{3}$
$V = \frac{4}{3} π (R_{o} A^{1 / 3})^{3}$
$V = \frac{4}{3} π R_{o}^{3} A$
Density of the nucleus is $ρ = \frac{M}{V}$
$ρ = \frac{m A}{\frac{4}{3} π R_{o}^{3} A}$
$ρ = \frac{3 m}{4 π R_{o}^{3}}$
Hence, nuclear density is independent of A.

Suggest Corrections

Similar questions

Q. In the study of Geiger-Marsdon experiment on scattering of

α

-particles by a thin foil of gold, draw the trajectory of

α

-particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study.
From the relation

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

, where

R_{0}

is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.
OR
Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction:

_{1}^{2} H +_{1}^{3} H ⟶_{2}^{4} H e + n

Using the data:

m (_{1}^{2} H) = 2.014102 u

m (_{1}^{3} H) = 3.016049 u

m (_{2}^{4} H e) = 4.002603 u

m_{n} = 1.008665 u

1 u = 931.5 M e V / c^{2}

Q. From the relation R =

R_{0} A^{\frac{1}{3}}

, where

R_{0}

is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Q. From the relation R = R0A1/3, where R0is a constant and A is themass number of a nucleus, show that the nuclear matter density isnearly constant (i.e. independent of A).

The unit of length convenient on the nuclear scale is a fermi : 1 f = 10^–
15m. Nuclear sizes obey roughly the following empirical relation :

where r is the radius of the nucleus, A its mass number, and r₀ is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

The unit of length convenient on the nuclear scale is a fermi : 1 f = 10^{– 15}m. Nuclear sizes obey roughly the following empirical relation :

Join BYJU'S Learning Program