  We consider the defocusing energy-critical inhomogeneous nonlinear
Schr\"{o}dinger equation (INLS) $iu_t + \Delta u = |x|^{-b}|u|^{k}u$ in
$\mathbb{R} \times \mathbb{R}^{n}$ where $n \geq 3$, $0<b<\min(2, n/2)$, and
$k=(4-2b)/(n-2)$. We show that for every spherically symmetric initial data
$\phi \in H^1(\mathbb{R}^n)$, or preferably $\dot{H}^1(\mathbb{R}^n)$, the
solution is globally well-posed and scatters for every such $n$ and $b$ except
for $n=4$ with $1\leq b<2$ and $n=5$ with $1/2\leq b\leq 5/4$. We mainly apply
the arguments of Tao (2005), but inspired by the work of Aloui and Tayachi
(2021), we utilize Lorentz spaces to define spacetime norms. This method is
distinct from the widespread concentration compactness principle and
establishes a quantitative bound for the solution's spacetime norm. The bound
has an exponential form $C\exp(CE[\phi]^C)$ in terms of the energy $E[\phi]$,
similar to Tao's work.
