1. A 67 kg water-skier is being pulled by a speedboat. The force causes her to accelerate at 3.8

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.

Marina86 [1]

Answer:

Therefore it will take 7.66 hours for 80% of the lead decay.

Explanation:

The differential equation for decay is

$\frac{dA}{dt}= kA$

$\Rightarrow \frac{dA}{A}=kdt$

Integrating both sides

ln A= kt+c₁

$\Rightarrow A= e^{kt+c_1}$

$\Rightarrow A=Ce^{kt}$ [ $e^{c_1}=C$ ]

The initial condition is A(0)= A₀,

$\therefore A_0=Ce^{0.k}$

$\Rightarrow C=A_0$

$\therefore A=A_0e^{kt}$ .........(1)

Given that the $Pb_{209}$ has half life of 3.3 hours.

For half life $A=\frac12 A_0$ putting this in equation (1)

$\frac12A_0=A_0e^{k\times3.3}$

$\Rightarrow ln(\frac12)= 3.3k$ [taking ln both sides, $ln \ e^a=a$ ]

$\Rightarrow k=\frac{ln \frac12}{3.3}$

⇒k= - 0.21

Now A₀= 1 gram, 80%=0.8

and A= (1-0.8)A₀ = (0.2×1) gram = 0.2 gram

Now putting the value of k,A and A₀in the equation (1)

$\therefore 0.2=1e^{(-0.21)\times t}$

$\Rightarrow e^{-0.21t}=0.2$

$\Rightarrow -0.21t= ln(0. 2)$

$\Rightarrow t= \frac{ln (0.2)}{-0.21}$

⇒ t≈7.66

Therefore it will take 7.66 hours for 80% of the lead decay.

3 0

3 years ago

ROY G BIV arranges the colors of the rainbow *

Elanso [62]

Answer:

Wavelengths..

Explanation:

The colors we see always go from red, which is least refracted, through orange, yellow, green, blue, indigo and violet -- Roy G Biv. The blue, indigo and violet wavelengths are refracted the most as sunlight passes through raindrops.

8 0

3 years ago

PLEASE ANSWER AS QUICKLY AS POSSIBLE THANK YOU SO MUCH

Harlamova29_29 [7]

Answer:

This description needs a unit describing the system of measurement.

6 0

2 years ago

The pka value for the carboxylic acid group in acetic acid is 4.75. write the predominant structure of acetic acid at (a ph=1, (

Scorpion4ik [409]

Hello!

A) At pH=1

This pH is lower than the value for the pKa, so Acetic acid wouldn't be ionized, but the equilibrium would be displaced to CH₃COOH

CH₃COOH ⇄ CH₃COO⁻ + H₃O⁺ (equilibrium displaced to the left)

The chemical structure for CH₃COOH is the first one in the attached images.

B) At pH=7

This pH is higher than the value for the pKa, so Acetic acid would be ionized, and the equilibrium would be displaced to CH₃COO⁻

CH₃COOH ⇄ CH₃COO⁻ + H₃O⁺ (equilibrium displaced to the right)

The chemical structure for CH₃COO⁻ is the second one in the attached images.

Have a nice day!

7 0

3 years ago

When a solution forms, what interactions between particles are involved? Which are exothermic? Which are endothermic?

Blizzard [7]

Answer:

Explanation:

There are three types of interactions involved between the particles when solution are formed.

1 : Solute - solute interaction:

2 : Solute - solvent interaction:

3 : Solvent - solvent interaction:

1 : Solute - solute interaction:

It is the inter-molecular attraction between the solute particles.

2 : Solute - solvent interaction:

It involve the inter-molecular attraction between solvent and solute particles.

3 : Solvent - solvent interaction:

It involve the intermolecular attraction between solvent particles.

Solutions are formed if the intermolecular attraction between solute particles are similar to the attraction between solvent particles.

Exothermic process:

The process will exothermic when solute solvent bonds are formed with the release of energy and energy required to brake the solute-solute particles and solvent solvent particles are less.

Endothermic process:

The process will be endothermic when energy required to break the solute-solute particles and solvent solvent particles are higher than energy released when solute solvent bonds are formed .

6 0

3 years ago