Answer
(a) The nuclear diameter of $^4He$ is $~~3.8~fm$
(b) The nuclear diameter of $^{56}Fe$ is $~~9.2~fm$
(c) The nuclear diameter of $^{238}U$ is $~~14.9~fm$
Work Step by Step
We can write a general equation for the radius $R$ of an atomic nucleus:
$R = r_0A^{1/3}$
$r_0 = 1.2~fm$
$A$ is the atomic mass number (number of nucleons)
We can write a general equation for the diameter $d$ of an atomic nucleus:
$d = 2R = 2r_0A^{1/3}$
(a) We can find the nuclear diameter of $^4He$:
$d = 2r_0A^{1/3}$
$d = (2)(1.2~fm)(4)^{1/3}$
$d = 3.8~fm$
(b) We can find the nuclear diameter of $^{56}Fe$:
$d = 2r_0A^{1/3}$
$d = (2)(1.2~fm)(56)^{1/3}$
$d = 9.2~fm$
(c) We can find the nuclear diameter of $^{238}U$:
$d = 2r_0A^{1/3}$
$d = (2)(1.2~fm)(238)^{1/3}$
$d = 14.9~fm$
