Nobelium -259 has a half life of 58 min? How much remains of 1kg sample after 1 day?
Use the formula.
A= Aö (1/2) t/h
This formula basically obtains the amount of sample remaining based on the number of half lives that have passed. In this case,
Ao = 1kg
t = 1 day = 24 hrs = 1440 min
h = 58 min
You have to find A. Plus in the values.
To find the solution
To use the formula A = A₀(1/2)^(t/h), we first need to find the number of half-lives in a day, since the given half-life is in minutes.
Since there are 24 hours in a day and 60 minutes in an hour, there are 24 * 60 = 1440 minutes in a day.
Next, we divide the total time (1 day) by the half-life (58 minutes) to find the number of half-lives:
Number of half-lives = 1440 minutes ÷ 58 minutes = 24.83 (approx.)
Since we cannot have partial half-lives, we will consider there are exactly 24 half-lives in 1 day.
Now we can calculate the amount remaining using the formula:
A = A₀(1/2)^(t/h)
where:
A = the amount remaining after a given time
A₀ = the initial amount
t = the total time
h = the half-life
Plugging in the values:
A = 1 kg * (1/2)^(24/1)
Now we can calculate the amount remaining:
A = 1 kg * (1/2)^24
A ≈ 9.31 x 10^(-8) kg
Therefore, after 1 day, approximately 9.31 x 10^(-8) kg remains from the 1 kg sample of nobelium-259.
To calculate the amount of Nobelium-259 remaining after 1 day, we can use the formula for exponential decay:
A = A₀ * (1/2)^(t/h)
where:
A is the amount remaining after a certain time period
A₀ is the initial amount
t is the time elapsed
h is the half-life
In this case, the half-life of Nobelium-259 is given as 58 minutes, so we need to convert the time period of 1 day into minutes.
There are 24 hours in a day, and each hour has 60 minutes. So, 1 day is equal to 24 * 60 = 1,440 minutes.
Now we can substitute the values into the formula:
A = 1 kg * (1/2)^(1,440/58)
To simplify the calculation, let's break it down step by step:
1. Calculate the fraction of time periods:
t/h = 1,440 minutes / 58 minutes = 24.8276
2. Calculate the remaining fraction of the substance:
(1/2)^(24.8276)
Using a calculator, we find that (1/2)^(24.8276) is approximately 0.000002129.
3. Calculate the remaining amount:
A = 1 kg * 0.000002129 = 0.000002129 kg
Therefore, after 1 day, approximately 0.000002129 kg (or about 2.129 micrograms) of the initial 1 kg sample of Nobelium-259 would remain.