The half-life of 42K is 12.4 hours. How much of a 750.0-gram sample is left after 62.0 hours?

Sagot :

Answer: 23 g

Explanation:

Amountafter = Amountbefore * (1/2)^(t/thalf)

Amountafter = (750 grams) * (1/2)^(62.0 hours/12.4 hours)

Amountafter = 23.4375 grams

750 has 2 significant digits

12.4 and 62.0 have 3 significant digits

So we take the lower of 2 significant digits:

23 grams

The half-life of 42K is 12.4 hours. 23.4375 grams of a 750 grams sample left after 62.0 hours.

What is Half Life ?

Half life is the amount of time required to reduce to one-half of its initial value. The symbol of half life is [tex]t_{1/2}[/tex].

How to calculate the remaining quantity when half life given ?

It is expressed as:

[tex]N(t) = N_{0} (\frac{1}{2})^{\frac{t}{t_{1/2}}[/tex]

where,

N(t) = quantity remaining

N₀ = initial quantity

t = elapsed time

[tex]t_{1/2}[/tex] = half-life of the substance

Here,

N₀ = 750.0 g

t = 62 hr

[tex]t_{1/2}[/tex] = 12.4

Now put the values in above equation we get

[tex]N(t) = N_{0} (\frac{1}{2})^{\frac{t}{t_{1/2}}[/tex]

[tex]N(t) = 750 \times (\frac{1}{2} )^{\frac{62}{12.4}}[/tex]

[tex]N(t) = 750 \times (\frac{1}{2})^5[/tex]

[tex]N(t) = 750 \times \frac{1}{32}[/tex]

N(t) = 23.4375 grams

Thus, from the above conclusion we can say that the 23.4375 grams of a 750 grams sample left after 62.0 hours.

Learn more about the Half life here: https://brainly.com/question/25750315

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