If the decay constant for radioactive decay of ^40 K is λ = 5.543*10^(-10) / year, use this equation to calculate ages of the samples in the following table:
t(1/2) = 0.693/λ
1)What is the half life of 40K?
table
-----Np --- Nd---- Nd/Np
A)6439-----2303---0.358
B)4395-----1303---0.300
C)8763-----1893---0.216
2)what are the half live elapsed and age in years for each sample?
To calculate the half-life of ^40K, we can use the equation:
t(1/2) = 0.693 / λ
where λ is the decay constant. Given that λ = 5.543 * 10^(-10) / year, we can substitute this value into the equation to find the half-life.
1) Half-life of ^40K:
t(1/2) = 0.693 / (5.543 * 10^(-10) / year)
t(1/2) ≈ 1.25 * 10^9 years
Therefore, the half-life of ^40K is approximately 1.25 billion years.
To calculate the age of each sample in the table, we can use the equation:
age = -t(1/2) * ln (Nd / Np)
where Nd and Np are the number of daughter atoms and parent atoms respectively. Given the values in the table, we can calculate the age for each sample.
2) Calculation of age for each sample:
A) Sample A:
age = - (1.25 * 10^9) * ln(2303 / 6439)
age ≈ 552 million years
B) Sample B:
age = - (1.25 * 10^9) * ln(1303 / 4395)
age ≈ 390 million years
C) Sample C:
age = - (1.25 * 10^9) * ln(1893 / 8763)
age ≈ 950 million years
Therefore, the half-life elapsed and age in years for each sample are as follows:
A) Half-life elapsed: 0.358 * 1.25 billion years
Age: Approximately 552 million years
B) Half-life elapsed: 0.300 * 1.25 billion years
Age: Approximately 390 million years
C) Half-life elapsed: 0.216 * 1.25 billion years
Age: Approximately 950 million years