Respuesta :
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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