13.Nuclei
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બે ન્યુકિલયસના પરમાણુદળાંકનો ગુણોત્તર $ 1:3$ છે. તેમની ન્યુકિલયર ઘનતાઓનો ગુણોત્તર કેટલો થાય?

A

${\left( 3 \right)^{\frac{1}{3}}}:1$

B

$1:1$

C

$1:3$

D

$3:1$

(AIPMT-2008)

Solution

હવે ઘનતા = (દળ/કદ) 

$\therefore$ ઘનતા  $\,\rho  = \frac{A}{{\frac{4}{3}\pi {R^3}}}\,$

$\therefore$ $\frac{{{\rho _{{A_1}}}}}{{{\rho _{{A_2}}}}} = \frac{{{A_1}}}{{\frac{4}{3}\pi R_1^3}} \times \frac{{\frac{4}{3}\pi R_2^3}}{{{A_2}}}\,\,\,\, $

$= \frac{{{A_1}}}{{{A_2}}} \times \frac{{R_2^3}}{{R_1^3}}$

 પણ ${\text{R}} = {{\text{R}}_{\text{0}}}{{\text{A}}^{\frac{{\text{1}}}{{\text{3}}}}}$ પરથી, 

${{\text{R}}^{\text{3}}} = {R_0}A\,\,\,$

$\therefore \,\,\,\frac{{{\rho _{{A_1}}}}}{{{\rho _{{A_2}}}}} = \frac{{{A_1}}}{{{A_2}}} \times \frac{{{A_2}}}{{{A_1}}} = 1:1$

Standard 12
Physics

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