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3 years ago

Iodine-131 half life 8.040 how long will it take for a 40 gram sample of iodine-131 to decay to 0.75 grams

Chemistry

1 answer:

otez555 [7]3 years ago

3 0

Answer:

See explanation below

Explanation:

To get this, we need to apply the general expression for half life decay:

N = N₀e(-λt) (1)

Where:

N and N₀ would be the final and innitial quantities, in this case, masses.

t: time required to decay

λ: factor related to half life

From the above expression we need λ and t. To get λ we use the following expression:

λ = t₁₂/ln2 (2)

And we have the value of half life, so, replacing we have:

λ = 8.04 / ln2 = 11.6

Now, we can replace in (1) and then, solve for t:

0.75 = 40 exp(-11.6t)

0.75 / 40 = exp(-11.6t)

ln(0.01875) = -11.6t

-3.9766 = -11.6t

t = -3.9766 / -11.6

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12. A beginner's bowling ball has a mass of 4.9 kg and a volume of 5.4 liters. Will it float in water,

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Taking into account the definition of density and Archimedes' principle, the beginner bowling ball will float on the water.

But first it is neccesary to know that density is a quantity referred to the amount of mass in a certain volume of a substance or a solid object.

In other words, the density is the relationship between the weight (mass) of a substance and the volume that the same substance occupies.

The expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

$density=\frac{mass}{volume}$

In this case, a beginner's bowling ball has a mass of 4.9 kg and a volume of 5.4 liters. This is:

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Replacing in the definition of density:

$density=\frac{4900 g}{5400 mL}$

Solving:

<u><em>density=0.907 </em></u> $\frac{g}{mL}$ <u><em /></u>

On the other hand, Archimedes' principle says that an object immersed in a liquid experiences an upward vertical force equal to the weight of the volume of the dislodged liquid.

The sinking or floating of an object is determined by its density with respect to that of the liquid in which it is submerged.

Considering water as the liquid where the object is submerged in this case, an object with a higher density than water will sink. In contrast, an object with a lower density than water will float.

In this case, considering that water has a density of 1 $\frac{g}{mL}$ , the bowling ball for beginners has a lower density. This indicates that, having a lower density than water, the object will float.

In summary, the beginner bowling ball will float on the water.

Learn more about density:

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