COMEDK 2023 Shift 1 Paper

To find the ratio of the radii RP:RQ of two nuclei with mass numbers AP=27 and AQ=125 respectively, we use the empirical formula for the radius of a nucleus, which is given by:
R=R0A1∕3
where R is the radius, A is the mass number of the nucleus, and R0 is a constant. Using this formula, we can express the radii of nuclei P and Q as:
‌RP=R0AP1∕3
‌RQ=R0AQ1∕3
To find the ratio RP:RQ, we divide the expression for RP by the expression for RQ :
‌

Rp

RQ

=‌

R0Ap1∕3

R0AQ1∕3

=‌

Ap1∕3

AQ1∕3

Substituting the given values of AP=27 and AQ=125, we get:
‌

Rp

RQ

=‌

271∕3

1251∕3

Since 27=33 and 125=53, the expression simplifies to:
‌

Rp

RQ

=‌

3

5

Therefore, the ratio of their radii RP:RQ is 3:5, which corresponds to Option