What is the mass number of a nucleus having a | vedclass

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

Question

(B) The radius of a nucleus is given by the formula $R = R_0 A^{1/3}$, where $R_0$ is a constant and $A$ is the mass number.Let $R_1$ be the radius of

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) The radius of a nucleus is given by the formula $R = R_0 A^{1/3}$, where $R_0$ is a constant and $A$ is the mass number.Let $R_1$ be the radius of the nucleus with mass number $A_1 = 189$, so $R_1 = R_0 (189)^{1/3}$.Let $R_2$ be the radius of the target nucleus with mass number $A_2$, so $R_2 = R_0 (A_2)^{1/3}$.According to the problem, $R_2 = \frac{1}{3} R_1$.Substituting the expressions, we get $R_0 (A_2)^{1/3} = \frac{1}{3} R_0 (189)^{1/3}$.Canceling $R_0$ from both sides, we have $(A_2)^{1/3} = \frac{1}{3} (189)^{1/3}$.Raising both sides to the power of $3$, we get $A_2 = (\frac{1}{3})^3 	imes 189$.$A_2 = \frac{1}{27} 	imes 189 = 7$.Therefore, the mass number is $7$.

Column-$I$	Column-$II$
$A$. Isotopes	$i$. $Li^7, Be^7$
$B$. Isobars	$ii$. $_8O^{18}, _9F^{19}$
$C$. Isotones	$iii$. $_1H^1, _1H^2$

What is the mass number of a nucleus having a radius equal to $\frac{1}{3}$ of that of ${}^{189}\text{Os}$?

Similar Questions

$A$ nucleus disintegrates into two smaller parts,which have their velocities in the ratio $3: 2$. The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$. The value of '$x$' is:

Match the following types of nuclei with their respective examples:
Column-$I$ Column-$II$
$A$. Isotopes $i$. $Li^7, Be^7$
$B$. Isobars $ii$. $_8O^{18}, _9F^{19}$
$C$. Isotones $iii$. $_1H^1, _1H^2$

The nuclear force between two nucleons is explained by

The mass number of a nucleus having a radius equal to half of the radius of a nucleus with mass number $192$ is:

The sodium nucleus $_{11}^{23}\text{Na}$ contains

Vedclass Test Series

Exam Paper Generator

Online Exam Module