If the ratio of the mass numbers of two nucle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The radius $R$ of a nucleus is related to its mass number $A$ by the formula $R = R_0 A^{1/3}$, where $R_0$ is a constant.The surface area $S$ of

Vedclass · Accepted Answer

$9 : 25$

Vedclass · Answer

(B) The radius $R$ of a nucleus is related to its mass number $A$ by the formula $R = R_0 A^{1/3}$, where $R_0$ is a constant.The surface area $S$ of a spherical nucleus is given by $S = 4 \pi R^2$.Substituting the expression for $R$, we get $S = 4 \pi (R_0 A^{1/3})^2 = 4 \pi R_0^2 A^{2/3}$.Thus, the surface area is proportional to $A^{2/3}$, i.e., $S \propto A^{2/3}$.Given the ratio of mass numbers $A_1 : A_2 = 27 : 125$, the ratio of their surface areas is $S_1 : S_2 = (A_1 / A_2)^{2/3}$.Substituting the values: $S_1 / S_2 = (27 / 125)^{2/3} = ((3^3) / (5^3))^{2/3} = (3/5)^2 = 9/25$.Therefore, the ratio of their surface areas is $9 : 25$.

If the ratio of the mass numbers of two nuclei is $27 : 125$, then the ratio of their surface areas is

Similar Questions

The ratio of the volume of an $Al^{27}$ nucleus to its surface area is (Given,$R_0 = 1.2 \times 10^{-15} \ m$):

The mass number of a nucleus is

The radius of an atom is of the order of $1\,\mathring{A}$ and the radius of a nucleus is of the order of $1$ fermi. How many magnitudes higher is the volume of the atom as compared to the volume of the nucleus?

The atomic weight of boron is $10.81$ and it has two isotopes $_5B^{10}$ and $_5B^{11}$. The ratio of $_5B^{10} : _5B^{11}$ in nature is:

If the radius of $_{13}^{27}Al$ is $3.6 \ fm$,then the radius of the $_{52}^{125}Te$ nucleus will be ........ $fm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module