Part A You are using a Geiger counter to measure the activity of a radioactive s

Question

Part A
You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 66.7 minutes , what is the half-life of this substance?

Part B

An unknown radioactive substance has a half-life of 3.20 hours . If 10.2 g of the substance is currently present, what mass A0 was present 8.00 hours ago?

Part C

Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years . How long will it take in years for 37.0 % of an Am-241 sample to decay?

Explanation / Answer

Part A.

For a first order reaction,

ln[A] - ln[Ao] = -kt

with,

Ao = 400

A = 100

t = 66.7min

k = rate constant = ?

we get,

ln(100) - ln(400) = -k x 66.7

k = 0.021 min-1

half life,

t1/2 = 0.693/k = 0.693/ = 33.34 min

Part A.

[A] = 10.2

[Ao] = initial mass = ?

t1/2 = 3.2 h

k = 0.693/3.2 = 0.22 h-1

t = 8 h

we get,

ln(10.2) + 0.22 x 8 = ln[Ao]

[Ao] = 59.28 g

Part C.

t1/2 = 432 y

k = 0.693/432 = 1.60 x 10^-3 y-1

37% sample decay mean, remaining sample = 100-37 = 63%

t = ?

we get,

ln(63) - ln(100) = -1.60 x 10^-3 x t

t = 288.8 y

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects