Question

$\large \orange {\underline {\underline {\tt Question :}}}$
The radius of nucleus $\sf ^{27}_{13}Al$ will be :

● Explanation required.
● Provide the proper steps.​

Answer 1

To Find :

We are asked to find radius of nucleus of $\sf ^{27}_{13}Al$ atom.

Solution :

❖ Nuclear radius of atom can be calculated by using the following formula!

$\dag\:\underline{\boxed{\bf{\orange{R_N=R_0\:A^{\frac{1}{3}}}}}}$

» $\sf{R_N}$ denotes radius of nucleus

» A denotes mass number

» $\sf{R_o}$ is a constant

• $\sf{R_o}=1.33\times10^{-13}\:cm$

♦ Mass number of $\bf{Al}$ = 27

By substituting the given values;

$\sf:\implies\:R_N=R_o\times A^{\frac{1}{3}}$

$\sf:\implies\:R_N=1.33\times 10^{-13}\times\sqrt[3]{27}$

$\sf:\implies\:R_N=1.33\times10^{-13}\times 3$

$\sf:\implies\:R_N=3.99\times 10^{-13}$

$:\implies\:\underline{\boxed{\bf{\gray{R_N\approx 4\times 10^{-13}\:cm}}}}$

Knowledge BoosteR :

• Alpha particles scattering demonstrated that the radius of nucleus was smaller that the radius of an atom by a factor of about 10⁴. So the volume of a nucleus is about 10‾¹² times the volume of the atom.
• The nucleus contains more than 99.9% of the mass of an atom.
• Electrons, protons & neutrons are the most important fundamental particles of atoms of all elements.
• The volume of the nucleus is very small and is only a minute fraction of the total volume of the atom.
• Nucleus has a diameter of the order of 10‾¹² to 10‾¹³ cm and the atom has a diameter of the order of 10‾⁸ cm.
• Thus, diameter (size) of the atom is 1,00,000 times the diameter of the nucleus.