Question 9

The energy of a single photon is given by $E_p = hf = 6 \times 10^{-34} \times 10^{15} = 6 \times 10^{-19}$ J.

The total energy of $N = 35 \times 10^7$ photons is $U = N E_p = 35 \times 10^7 \times 6 \times 10^{-19} = 210 \times 10^{-12}$ J.

Since the volume $V = 1 \text{ m}^3$, the energy density $u$ is $u = \frac{U}{V} = 210 \times 10^{-12} \text{ J/m}^3$.

For an electromagnetic wave, the average energy density is related to the amplitude of the magnetic field $B_0$ by: $u = \frac{B_0^2}{2\mu_0}$

Substituting the values: $210 \times 10^{-12} = \frac{B_0^2}{2 \times 4\pi \times 10^{-7}}$ $B_0^2 = 210 \times 10^{-12} \times 8 \times \frac{22}{7} \times 10^{-7}$ $B_0^2 = 30 \times 8 \times 22 \times 10^{-19} = 5280 \times 10^{-19} = 528 \times 10^{-18}$ $B_0 = \sqrt{528} \times 10^{-9} \text{ T}$

Comparing with $B_0 = \alpha \times 10^{-9}$ T: $\alpha = \sqrt{528} \approx 22.978$

Rounding to the nearest integer as per the provided range, $\alpha = 23$.