c. Write down the relationship between refracting angle A of a triangle and minimum deviation Dm and…

Question

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

ScanSolve AI Tutor · Accepted Answer

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: $N = \frac{2}{3} N_0$ and $t = 32$ days.

Use the radioactive decay formula.
$N = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}}$
Substitute the given values.
$\frac{2}{3} N_0 = N_0 \left(\frac{1}{2}\right)^{32/T_{1/2}}$
Divide both sides by $N_0$ .
$\frac{2}{3} = \left(\frac{1}{2}\right)^{32/T_{1/2}}$
Take the natural logarithm (or logarithm to any base) of both sides.
$\ln\left(\frac{2}{3}\right) = \ln\left(\left(\frac{1}{2}\right)^{32/T_{1/2}}\right)$ $\ln(2) - \ln(3) = \frac{32}{T_{1/2}} (\ln(1) - \ln(2))$ $\ln(2) - \ln(3) = -\frac{32}{T_{1/2}} \ln(2)$
Solve for $T_{1/2}$ .
$T_{1/2} = -\frac{32 \ln(2)}{\ln(2) - \ln(3)}$ $T_{1/2} = -\frac{32 \times 0.6931}{0.6931 - 1.0986}$ $T_{1/2} = -\frac{22.1792}{-0.4055}$ $T_{1/2} \approx 54.695 \text{ days}$
The half-life is $\boxed{\text{54.7 days}}$ (to 3 significant figures).

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

Step-by-step solution

Use the radioactive decay formula.

Substitute the given values.

Divide both sides by $N_0$ .

Take the natural logarithm (or logarithm to any base) of both sides.

Solve for $T_{1/2}$ .

Still stuck on this one?

More Physics Questions

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

Step-by-step solution

Use the radioactive decay formula.

Substitute the given values.

Divide both sides by N0N_0N0​.

Take the natural logarithm (or logarithm to any base) of both sides.

Solve for T1/2T_{1/2}T1/2​.

Still stuck on this one?

More Physics Questions

Divide both sides by $N_0$ .

Solve for $T_{1/2}$ .