Question

t the beginning of an experiment; scientist has 280 grams of radioactive goo. After 75 minutes; her sample has decayed to 17.5 grams What is the half-life ofthe goo in minutes? Preview Find formula for G(t). the amount of goo remaining at time t Previen How many grams of goo will remain after mnutes _ Previen You may enter the exact value Or round to decimal places

Answer 1

After 75 minutes, a sample of 280 grams of radioactive goo has decayed to 17.5 grams. The half-life of the radioactive is 18.75 minutes.

The problem can be solved using decay model. The formula of decay system is given by:

Nt = No . e^(-λ . t)

Where:

Nt = quantity at time t

No = initial quantity

λ = decay constant = ln(2) / T

T = half life

The above formula can be rearranged to:

T = t . ln(2) / [ln(No/Nt)]

Parameters given in th problem:

No = 280 grams

t = 75 minutes

Nt = 17.5 grams

Plug these parameters into the formula:

T =  75 . ln(2) / [ln(280/17.5)]

  = 18.75 minutes

Hence, the half-life of the radioactive goo is 18.75 minutes.

Learn more about decay system here:

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