The ratio of the nuclear radii of {}^{135}Cs | vedclass

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Question

(B) The nuclear radius $R$ is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.Therefore,the ratio of the r

Vedclass · Accepted Answer

$1.50$

Vedclass · Answer

(B) The nuclear radius $R$ is given by the formula $R = R_0 A^{1/3}$,where $R_0$ is a constant and $A$ is the mass number.Therefore,the ratio of the radii is given by $\frac{R_{Cs}}{R_{Ca}} = \left( \frac{A_{Cs}}{A_{Ca}} \right)^{1/3}$.Substituting the given mass numbers $A_{Cs} = 135$ and $A_{Ca} = 40$:$\frac{R_{Cs}}{R_{Ca}} = \left( \frac{135}{40} \right)^{1/3}$.Simplifying the fraction inside the bracket by dividing both numerator and denominator by $5$:$\frac{135}{40} = \frac{27}{8}$.Thus,$\frac{R_{Cs}}{R_{Ca}} = \left( \frac{27}{8} \right)^{1/3} = \frac{3}{2} = 1.50$.

The ratio of the nuclear radii of ${}^{135}Cs$ to ${}^{40}Ca$ is:

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