To determine the nuclear radius of
‌125‌Fe, we need to use the relationship between nuclear radius and mass number. The nuclear radius
(R) of a nucleus is given by the empirical formula:
R=R0A1∕3where:
R0 is the proportionality constant (approximately
1.2−1.3 fermi) and
A is the mass number (number of nucleons).
Given the nuclear radius of
‌27‌Al (Aluminium-27) is 3.6 fermi, we can use this to find
R0 :
R27‌Al=R0⋅271∕3We know:
R2τ‌Al=3.6‌ fermi ‌Therefore:
‌3.6=R0⋅271∕3‌R0=‌We can solve for
R0 :
‌271∕3=3‌R0=‌=1.2‌ fermi ‌ Now, using this
R0, we find the radius of
‌125‌Fe (Iron-125):
R125‌Fe=R0⋅1251∕3Substitute
R0 :
R125‌Fe=1.2⋅1251∕3We need to find
1251∕3 :
1251∕3=5 Therefore:
R125‌Fe=1.2⋅5=6‌ fermi ‌Converting fermi to meters (since 1 fermi
=10−15 meters):
6‌ fermi ‌=6×10−15‌ meters ‌The correct option is:
Option C
6×10−15m