c. Write down the relationship between refracting angle A of a triangle and minimum deviation Dm and refractive index. d. Show that the pressure on a single molecule of a gas inside a box is given by p = (1/3)ρc2 where ρ = density, c = speed

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Asked on June 1, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-06-01T08:16:12.115Z

My apologies, the previous answer was cut off. Let's finish 12. f. ii. 12. f. ii. Two-thirds of a radioactive nucleus remained after 32 days of decays. Calculate the half-life. Let N_0 be the initial number of nuclei and N be the number of nuclei remaining. Given: N = (2)/(3) N_0 and t = 32 days. Step 1: Use the radioactive decay formula. N = N_0 ((1)/(2))^t/T_1/2 Step 2: Substitute the given values. (2)/(3) N_0 = N_0 ((1)/(2))^32/T_1/2 Step 3: Divide both sides by N_0. (2)/(3) = ((1)/(2))^32/T_1/2 Step 4: Take the natural logarithm (or logarithm to any base) of both sides. ((2)/(3)) = (((1)/(2))^32/T_1/2) (2) - (3) = (32)/(T_1/2) ((1) - (2)) (2) - (3) = -(32)/(T_1/2) (2) Step 5: Solve for T_1/2. T_1/2 = -(32 (2))/((2) - (3)) T_1/2 = -(32 × 0.6931)/(0.6931 - 1.0986) T_1/2 = -(22.1792)/(-0.4055) T_1/2 ≈ 54.695 days The half-life is 54.7 days (to 3 significant figures). 3 done, 2 left today. You're making progress.

Accepted Answer · 2026-06-01T08:16:12.115Z

My apologies, the previous answer was cut off. Let's finish 12. f. ii. 12. f. ii. Two-thirds of a radioactive nucleus remained after 32 days of decays. Calculate the half-life. Let N_0 be the initial number of nuclei and N be the number of nuclei remaining. Given: N = (2)/(3) N_0 and t = 32 days. Step 1: Use the radioactive decay formula. N = N_0 ((1)/(2))^t/T_1/2 Step 2: Substitute the given values. (2)/(3) N_0 = N_0 ((1)/(2))^32/T_1/2 Step 3: Divide both sides by N_0. (2)/(3) = ((1)/(2))^32/T_1/2 Step 4: Take the natural logarithm (or logarithm to any base) of both sides. ((2)/(3)) = (((1)/(2))^32/T_1/2) (2) - (3) = (32)/(T_1/2) ((1) - (2)) (2) - (3) = -(32)/(T_1/2) (2) Step 5: Solve for T_1/2. T_1/2 = -(32 (2))/((2) - (3)) T_1/2 = -(32 × 0.6931)/(0.6931 - 1.0986) T_1/2 = -(22.1792)/(-0.4055) T_1/2 ≈ 54.695 days The half-life is 54.7 days (to 3 significant figures). 3 done, 2 left today. You're making progress.

c. Write down the relationship between refracting angle A of a triangle and minimum deviation Dm and refractive index. d. Show that the pressure on a single molecule of a gas inside a box is given by p = (1/3)ρc2 where ρ = density, c = speed

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c. Write down the relationship between refracting angle A of a triangle and minimum deviation Dm and refractive index. d. Show that the pressure on a single molecule of a gas inside a box is given by p = (1/3)ρc2 where ρ = density, c = speed

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