isotope chromium -51 has a half life of 28 days. If the original sample had a mass of 28.0 grams, what mass of chromium -51 sample remains after 84 days?

k = 0.693/t1/2

Substitute and solve for k and use k in the equation below.

ln(No/N) = kt
No = 28
N = ?
k from above
t = 84 days.

The isotope chromium-51 has a half-life of 28 days. If the original sample had a mass of 28.0 grams, what mass of the chromium-51 sample remains after 84 days?

To determine the mass of the chromium-51 sample remaining after 84 days, we need to calculate the number of half-lives that have elapsed during this time period.

The formula to calculate the number of half-lives is:

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

In this case, the total time elapsed is 84 days, and the half-life of chromium-51 is 28 days.

Number of half-lives = 84 days / 28 days = 3 half-lives

Now, we can calculate the remaining mass using the following formula:

Remaining mass = Initial mass * (1/2)^(Number of half-lives)

Substituting the values into the formula:

Remaining mass = 28.0 grams * (1/2)^(3 half-lives)

Calculating:

Remaining mass = 28.0 grams * (1/2)^3 = 28.0 grams * (1/8) = 3.5 grams

Therefore, after 84 days, the mass of chromium-51 remaining is 3.5 grams.

To calculate the mass of the chromium-51 sample that remains after 84 days, we can use the formula for exponential decay:

N(t) = N₀ * (1/2)^(t / t_(1/2))

Where:
N(t) is the remaining amount of the sample after time t
N₀ is the initial amount of the sample
t is the elapsed time
t_(1/2) is the half-life of the isotope

In this case, the initial amount (N₀) is 28.0 grams, the half-life (t_(1/2)) is 28 days, and the elapsed time (t) is 84 days.

Now we can plug these values into the formula and solve for N(84):

N(84) = 28.0 * (1/2)^(84 / 28)

Calculating the exponent:

(84 / 28) = 3

N(84) = 28.0 * (1/2)^3
= 28.0 * (1/8)
= 3.5 grams

Therefore, after 84 days, there would be approximately 3.5 grams of chromium-51 remaining from the original 28.0 grams sample.