What is the mass of an original 5.60-gram sample of iron-53 that remains unchanged after 25.53 minutes? (1) 0.35g
(2) 1.40 g(3) 0.70 g
(4) 2.80 g

After 25.53 minutes there will remain 0.70 grams of the iron-53 sample. Option 3 is correct.

Explanation:

Step 1: Data given

Original mass of the original iron sample = 5.60 grams

Half life of iron-53 = 8.5167 minutes

Step 2: Calculate the rate constant

k = (ln 2)/(t1/2)

⇒ with k = the rate constant

⇒ with t1/2 = the half-life time = 8.5167 minutes

k = 0.08139 / min

Step 3: Calculate the mass after 25.53 minutes

At = A0*e^(-kt)

⇒ with At = the amount of iron sample after 25.53 minutes

⇒ A0 = the initial amount of iron sample =5.50 grams

⇒ with k =  0.08139 / min

⇒ with t = the time = 25.53 minutes

At = 5.50*e^(-0.08139*25.53)

At = 0.70 grams

After 25.53 minutes there will remain 0.70 grams of the iron-53 sample

i believe it is c.) 1575 j.