1. Use the energy density formula for an electromagnetic wave

In vacuum, the average total energy density of a plane electromagnetic wave is

$u = \frac{B_0^2}{2\mu_0}$

where $B_0$ is the amplitude of the magnetic field.

So,

$B_0 = \sqrt{2\mu_0 u}$

2. Express $\mu_0$ using the given data

We know

$c^2 = \frac{1}{\mu_0 \varepsilon_0} \implies \mu_0 = \frac{1}{\varepsilon_0 c^2}$

Also,

$\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9$

Hence,

$\varepsilon_0 = \frac{1}{4\pi \times 9 \times 10^9}$

So,

$\mu_0 = 4\pi \times 10^{-7}\, \text{H/m}$

3. Substitute values

Given:

$u = 1.02 \times 10^{-8}\, \text{J/m}^3$

Therefore,

$B_0 = \sqrt{2 \times 4\pi \times 10^{-7} \times 1.02 \times 10^{-8}}$

$B_0 = \sqrt{8\pi \times 1.02 \times 10^{-15}}$

Now,

$8\pi \times 1.02 \approx 25.63$

So,

$B_0 = \sqrt{25.63 \times 10^{-15}}$

$B_0 \approx 5.06 \times 10^{-7.5}$

More directly,

$B_0 \approx 1.60 \times 10^{-7}\, \text{T}$

4. Convert to nT

Since

$1\,\text{nT} = 10^{-9}\,\text{T}$

we get

$B_0 = 1.60 \times 10^{-7} \,\text{T} = 160 \times 10^{-9} \,\text{T} = 160\,\text{nT}$

5. Match with the options

$\boxed{160\,\text{nT}}$

So the correct option is C.