Radius of nucleus may be given as $R_{N} = R_{0} A^{1 / 3}$ , where $A =$ mass number and $R_{0} =$ constant. Show that the nuclear matter density is nearly constant. $R_{0} = 1.2 \times 10^{- 15}$ .

Open in App

Solution

Radius of a nucleus of mass number is given by
R= $R_{0} A^{1 / 3}$

Where, $R_{0}$ = 1.2 x $1 0^{- 15}$ m

This implies that the volume of the nucleus is proportional to $R^{3}$ is proportional to A.

Volume of nucleus= $\frac{4}{3} π r^{3}$

=+ $d \frac{4}{3} π (R_{0} A^{1 / 3})^{3}$

= $\frac{4}{3} π R_{0}^{3} A$

Density of nucleus= $\frac{m a s s o f n u c l e u s}{v o l u m e o f n u c l e u s}$

= $\frac{m a}{\frac{4}{3} π R_{0}^{3} A}$

= $\frac{3 m}{4 π R_{0}^{3}}$

This equation shows that the density of nucleus is constant, independent of A for all nuclei.

Suggest Corrections

Similar questions

Q. Radius of nucleus may be given as

R_{N} = R_{0} . A^{1 / 3}

, where

A = m a s s n u m b e r

and

R_{0} = C o n s t a n t

. Calculate the density of nucleus of an atom if

R_{0} = 1.2 \times 10^{- 15}

[N_{A} = 6 t i m e s 10^{23} \times 8 π \times (1.2)^{3}

1000

From the relation R = R₀A¹/³, where R₀ 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).

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 :

Q. The potential of an atom is given by

V = V_{0} l o g_{e} (r / r_{0})

where

r_{0}

is a constant and r is the radius of the orbit. Assuming Bohr's model to be applicable, which variation of

r_{n}

with n is possible (n being principal quantum number)?

Join BYJU'S Learning Program

Radius of nucleus may be given as RN=R0A1/3, where A= mass number and R0= constant. Show that the nuclear matter density is nearly constant. R0=1.2×10−15.

Radius of nucleus may be given as $R_{N} = R_{0} A^{1 / 3}$ , where $A =$ mass number and $R_{0} =$ constant. Show that the nuclear matter density is nearly constant. $R_{0} = 1.2 \times 10^{- 15}$ .