# The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decompose after 5.55 days if the sample initially weighs 100.0 grams?

After 5.55 days, 63.4 g of radon will have decayed.

A first-order process's half-life can be calculated using the formula

A first-order process's integrated formula is

If 36.55 g are still present, the mass that broke down is

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To find the amount of radon decomposed after 5.55 days, use the first-order decay equation:

[ A = A_0 \times e^{-\lambda t} ]

Where:

- ( A ) is the final amount of radon after ( t ) days
- ( A_0 ) is the initial amount of radon
- ( \lambda ) is the decay constant
- ( t ) is the time in days

Given:

- ( A_0 = 100.0 ) grams
- ( t = 5.55 ) days
- Half-life ( T_{1/2} = 3.823 ) days

First, calculate the decay constant ( \lambda ) using the half-life formula:

[ T_{1/2} = \frac{\ln(2)}{\lambda} ]

Then, plug in the values to find ( \lambda ). Once you have ( \lambda ), use it in the decay equation to find ( A ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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