How much of a 849 gram sample of Potassium-42 will remain after 62 hours?

To find out how much of a 849 gram sample of Potassium-42 will remain after 62 hours, we can use the formula for exponential decay based on half-lives.

1. Calculate the number of half-lives that have passed in 62 hours:

– Half-life of Potassium-42 = 12.4 hours

– Number of half-lives = Total time / Half-life

– Number of half-lives = 62 hours / 12.4 hours ≈ 5

2. Use the half-life to find the remaining amount:

– The formula for the remaining amount after ( n ) half-lives is:

[ text{Remaining amount} = text{Initial amount} times left(frac{1}{2}right)^n ]

– Plug in the values:

[ text{Remaining amount} = 849 , text{grams} times left(frac{1}{2}right)^5 ]

– (left(frac{1}{2}right)^5 = frac{1}{32})

– Therefore:

[ text{Remaining amount} = 849 , text{grams} times frac{1}{32} approx 26.53 , text{grams} ]

So, after 62 hours, approximately 26.53 grams of

To calculate the remaining amount of Potassium-42 after 62 hours, we can use the formula for radioactive decay:

[ N = N_0 left( frac{1}{2} right)^{frac{t}{t_{1/2}}} ]

Where:

– ( N ) is the remaining amount,

– ( N_0 ) is the initial amount (849 grams),

– ( t ) is the total time elapsed (62 hours),

– ( t_{1/2} ) is the half-life (12.4 hours).

1. First, calculate how many half-lives fit into 62 hours:

[ frac{62 text{ hours}}{12.4 text{ hours/half-life}} approx 5 text{ half-lives} ]

2. Now, substitute into the formula:

[ N = 849 left( frac{1}{2} right)^{5} ]

3. Calculate ( left( frac{1}{2} right)^{5} ):

[ left( frac{1}{2} right)^{5} = frac{1}{32} ]

4. Now calculate the remaining amount:

[ N = 849 times frac{1}{32} approx 26.53 text{ grams} ]

So, after 62 hours