1. Use the relation between wavelength and frequency

For electromagnetic waves, $f = \frac{c}{\lambda}$ where $c = 3\times 10^8\ \text{m/s}, \qquad \lambda = 960\ \text{m}$

So, $f = \frac{3\times 10^8}{960} = 3.125\times 10^5\ \text{Hz}$

2. Condition for resonance of an LC circuit

At resonance, $f = \frac{1}{2\pi\sqrt{LC}}$

Hence, $L = \frac{1}{(2\pi f)^2 C}$

Given capacitance: $C = 2.56\ \mu F = 2.56\times 10^{-6}\ \text{F}$

3. Substitute the values

Using $L = \frac{1}{4\pi^2 f^2 C}$

Now, $f^2 = (3.125\times 10^5)^2 = 9.765625\times 10^{10}$

So, $L = \frac{1}{4\pi^2 \times 9.765625\times 10^{10} \times 2.56\times 10^{-6}}$

Using $\pi^2 \approx 9.87$, $4\pi^2 \approx 39.48$

Also, $9.765625\times 10^{10} \times 2.56\times 10^{-6} = 2.5\times 10^5$

Therefore, $L = \frac{1}{39.48\times 2.5\times 10^5}$ $L = \frac{1}{9.87\times 10^6}$ $L \approx 1.013\times 10^{-7}\ \text{H}$

4. Match with the asked form

The inductance is $L \approx 10.13\times 10^{-8}\ \text{H}$

So the required integer is $\boxed{10}$

5. Comparison with stored answer

Derived answer = $10$

Stored correct answer = $10$

Hence, they agree.