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Tems11 [23]
2 years ago
14

What is the half-life of polonium-210 if it takes 828 days for a sample to be reduced to 1.6% of its original mass?

Chemistry
1 answer:
vagabundo [1.1K]2 years ago
4 0

Answer:

The half-life of polonium-210 is approximately 138.792 days.

Explanation:

We must remember that the decay of a radioisotope is modelled by this ordinary differential equation:

\frac{dm}{dt} = -\frac{m(t)}{\tau}

Where:

m(t) - Current mass of the isotope, measured in grams.

\tau - Time constant, measured in days.

Whose solution is:

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }

Where m_{o} is the initial mass of the isotope, measured in grams.

Our first step is to determine the value of the time constant:

-\frac{t}{\tau} = \ln \frac{m(t)}{m_{o}}

\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }

If we know that \frac{m(t)}{m_{o}} = 0.016 and t = 828\,days, then the time constant of the radioisotope is:

\tau = -\frac{828\,days}{\ln 0.016}

\tau \approx 200.234\,days

And lastly we find the half-life of polonium-210 (t_{1/2}), measured in days, by using this expression:

t_{1/2} = \tau \cdot \ln 2

t_{1/2} = (200.234\,days)\cdot \ln 2

t_{1/2}\approx 138.792\,days

The half-life of polonium-210 is approximately 138.792 days.

You might be interested in
Phosphorus-32 is radioactive and has a half life of 14.3 days. What percentage of a sample would be left after 12.6 days
nadya68 [22]

Answer:

There is 54.29 % sample left after 12.6 days

Explanation:

Step 1: Data given

Half life time = 14.3 days

Time left = 12.6 days

Suppose the original amount is 100.00 grams

Step 2: Calculate the percentage left

X = 100 / 2^n

⇒ with X = The amount of sample after 12.6 days

⇒ with n = (time passed / half-life time) = (12.6/14.3)

X = 100 / 2^(12.6/14.3)

X = 54.29

There is 54.29 % sample left after 12.6 days

8 0
2 years ago
Given that you have 14.5 moles of n2, how many moles of h2 are theoretically needed to produce 30.0 moles of nh3 according to re
erastovalidia [21]

45 moles of H₂ are theoretically needed to produce 30.0 moles of NH₃

<h3>Further explanation</h3>

Stoichiometry in Chemistry learn about chemicals mainly emphasizes quantitative, such as the calculation of volume, mass, number, which is related to numbers, molecules, elements, etc.

A reaction coefficient is a number in the chemical formula of a substance involved in the reaction equation. The reaction coefficient is useful for equalizing reagents and products.

In the reaction there are also manifestations of reagent substances namely gas (g), liquid (liquid / l), solid (solid / s) and solution (aqueous / aq).

The concentration of a substance can be expressed in several quantities such as moles, percent (%) weight/volume,), molarity, molality, parts per million (ppm) or mole fraction. The concentration shows the amount of solute in a unit of the amount of solvent.

  • Mole

The mole itself is the number of particles contained in a substance amounting to 6.02.10²³

Mole can also be sought if the amount of substance mass and its molar mass is known

\large{\boxed{\boxed{\bold{mol=\frac{mass}{molar\:mass}}}}

 

Reaction that happens :

N₂ +3H₂ ⇒ 2NH₃

mole N₂ : H₂ : NH₃ = 1 : 3 : 2

To produce 30.0 moles of NH₃,

  • H₂ needed :

mole~H_2~=~\frac{3}{2}\times~30~mole

mole H₂ = 45 mole

  • N₂ needed :

mole~N_2~=~\frac{1}{2}~\times~30

mole N₂ = 15 mole

So the minimum N₂ needed is: 15 mole

14.5 moles of N₂ can only produce NH₃ :

mole~NH_3~=~\frac{2}{1}~\times~14.5

mole NH₃ = 29 mole

<h3>Learn more </h3>

The mass of one mole of raindrops

brainly.com/question/5233234

moles of NaOH

brainly.com/question/4283309

moles of water you can produce

brainly.com/question/1405182

 

Keywords: mole,  NH₃, N₂, H₂

7 0
3 years ago
Read 2 more answers
HELP
tatiyna

Answer:

Bi (Bismuth)

Ag (Silver)

Li (Lithium)

Explanation:

Xe (Xenon) and I (Iodine) are non-metals. They cannot from a metallic bond because metallic bonds are bonds between metals only.

7 0
2 years ago
Science Chemical compound formula​
Flura [38]

Answer:

NaCl (common salt)

Explanation:

it is called sodium chloride

4 0
3 years ago
Which state of matter is being described below? it can be squashed easily, spreads out slowly, has low density,
sergeinik [125]

Answer:

liquid

Explanation:

Gas has very low density but spreads fast. Solid has high density.

3 0
2 years ago
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