Which of the following units is an SI base unit?

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

I need help with the 2nd part first gets brainlist

mixer [17]

Answer:

7. 4H₂O

Elements: Hydrogen, Oxygen

Number of molecules: 4

Number of elements: 8 H, 4 O

Number of Atoms: 12

Explanation:

The elements are determined by the their symbol i.e. H = hydrogen.

The number of molecules is determined by the coefficient ( the number in front of everything, in this case 4).

The number of elements is determined by the coefficient and the subscripts. Multiply the coefficient by the subscript after each element. When there is no subscript, it is equal to 1. 4H₂ = 4x2 = 8; 4O = 4x1 = 4.

The number of atoms is all the individual elements added together. 8+4 = 12.

8 0

3 years ago

Explain the difference between heat and temperature. Does 1 L of water at 658°F have more, less, or the same quantity of energy

pogonyaev

The answer is- The energy of 1 L water at temperature 347.78 °C have more energy as 1 L of water at temperature 65°C.

Heat is a type of energy that causes a person's body to feel hot or cold.

While the temperature of an object is a parameter that indicates how hot or cold the object is.

How is the temperature in degree Fahrenheit converted to degree celsius?

To convert the temperature in Fahrenheit to Celsius, subtract 32 and multiply by 5/9.

° $C =( ^0F -32) * \frac{5}{9}$

Now, heat is a form of energy that flows from hotter object to colder object and temperature indicates whether the object is hot or cold by measuring its average kinetic energy.
Now, the given temperature of 1 L water is 658 °F. This temperature in degree celsius is calculated as-

°C $= (658 F-32) *\frac{5}{9} = 347.78 \° C$