Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?
k = 0.693/t1/2
k has units of yr^-1
Convert 3.10 mg sample to moles.
moles = grams/molar mass.
Convert moles to atoms.
# atoms = moles x 6.02E23
rate = k*Number atoms
This will give you the rate in a year (decays per year). Convert to 190 seconds for the number of decays in that time.
Divide by 190 seconds to obtain dps (decays per second). That will be the number of Bq.
To determine the number of beta particles emitted in 190 seconds by a sample of Cobalt-60 (Co-60), you need to use the decay constant and the decay equation. Let's break down the steps to find the answer.
Step 1: Calculate the decay constant (λ)
The decay constant (λ) is related to the half-life (t1/2) by the formula λ = (ln(2)) / t1/2, where ln is the natural logarithm. In this case, the half-life of Co-60 is given as 5.26 years. We need to convert it to seconds for further calculations.
t1/2 (in seconds) = 5.26 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute
Step 2: Calculate the number of beta particles emitted (N) using the decay equation
The general decay equation is N(t) = N₀ * e^(-λt), where N₀ is the initial number of particles, t is the time, and N(t) is the number of particles at time t.
For this question, we need to find N(190s) since we want the number of beta particles emitted in 190 seconds.
Step 3: Calculate the activity of the sample (A) in becquerels (Bq)
Activity (A) is the rate at which radioactive decay occurs. It is measured in becquerels (Bq), where 1 Bq is equivalent to 1 decay per second.
The activity can be calculated using the following formula: A = λ * N₀, where A is the activity and λ is the decay constant.
Now, let's perform the calculations:
Step 1: Calculate the decay constant (λ)
t1/2 = 5.26 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute
λ = (ln(2)) / t1/2
Step 2: Calculate the number of beta particles emitted (N)
N(t) = N₀ * e^(-λt)
N(190s) = N₀ * e^(-λ * 190)
Step 3: Calculate the activity of the sample (A) in Bq
A = λ * N₀
To calculate these values, we need additional information: the initial number of particles (N₀). Please provide the initial number of particles in the sample of Co-60.