Question 21: Atoms & Nuclei

Question

If the mass numbers of two nuclei are in the ratio $5: 2$ and their diameters are in ratio $2: 6$. Then their nuclear densities will be in the ratio

Accepted Answer

LetÃ¢ÂÂs denote the two nuclei by 1 and 2.  Recall that
Ã¢ÂÂ Mass Ã¢ÂÂ A (mass number)
Ã¢ÂÂ Volume Ã¢ÂÂ RÃÂ³ Ã¢ÂÂ (Diameter)ÃÂ³
So
$$ ÃÂ_1/ÃÂ_2 \;=\;\frac{A_1/V_1}{A_2/V_2} \;=\;\frac{A_1/A_2}{(D_1/D_2)^3} \;=\;\frac{	frac{5}{2}}{\bigl(	frac{2}{6}\bigr)^3} \;=\;\frac{5/2}{(1/3)^3} \;=\;(5/2)	imes27 \;=\;\frac{135}{2} \;\approx\;67.5\!:1 $$
None of the given choices match 135 : 2, but in the liquidÃ¢ÂÂdrop model of the nucleus one shows that
$$R\propto A^{1/3}\quad\Longrightarrow\quadÃÂ\;=\;\frac{A}{R^3}\;\approx\;	ext{constant}$$
for all nuclei.  Hence to very good approximation
$$ÃÂ_1:ÃÂ_2\;=\;1:1$$
Answer: Option A (1 : 1).

Answer

$1: 1$

Answer

$2: 5$

Answer

$10: 12$

Answer

$6: 5$

Atoms & Nuclei

If the mass numbers of two nuclei are in the ratio 5: 2 and their diameters are in ratio 2: 6. Then their nuclear densities will be in the ratio

Choose the correct answer: