1. **Problem 1: Compare the size of a proton to the distance to GN-z11 in terms of order of magnitude.** The size of a proton is about 1 femtometer (fm), where 1 fm = $10^{-15}$ meters. The distance to GN-z11 is approximately $32 \times 10^9$ light years (from typical astronomical data). First, convert the distance to meters: - 1 light year = $9.461 \times 10^{15}$ meters - Distance to GN-z11 = $32 \times 10^9 \times 9.461 \times 10^{15} = 3.02752 \times 10^{26}$ meters Now, take the ratio of the distance to the proton size: $$\text{Ratio} = \frac{3.02752 \times 10^{26}}{1 \times 10^{-15}} = 3.02752 \times 10^{41}$$ The order of magnitude difference is about $10^{41}$. 2. **Problem 2: Convert energy usage from $3 \times 10^8$ kg (m/s)$^2$ to kilowatt-hours (kWh).** Note: kg (m/s)$^2$ is not a standard energy unit. Assuming the user means $3 \times 10^8$ joules (J) since 1 J = 1 kg m$^2$/s$^2$. Conversion factor: - 1 kWh = $3.6 \times 10^6$ J Calculate energy in kWh: $$\text{kWh} = \frac{3 \times 10^8}{3.6 \times 10^6} = \frac{3}{3.6} \times 10^{8-6} = 0.8333 \times 10^2 = 83.33$$ So, the energy used daily is approximately 83.33 kWh. **Final answers:** - Order of magnitude difference between proton size and GN-z11 distance: $10^{41}$ - Energy usage in kWh: approximately 83.33 kWh