What mass of ¹⁴C,with a half-life of 5730 y,do you need to provide a decay rate of
The mass of ¹⁴C is 14.00 u,and 1 u = 1.6605 × 10^-27 kg.

Question

What mass of ¹⁴C,with a half-life of 5730 y,do you need to provide a decay rate of The mass of ¹⁴C is 14.00 u,and 1 u = 1.6605 × 10^-27 kg.

Quizplus · Accepted Answer

We can use the decay rate equation:

λ = ln(2)/t₁/₂

where λ is the decay constant and t₁/₂ is the half-life. Rearranging this equation, we get:

N = (λ*N₀)/λ

where N is the final number of atoms, N₀ is the initial number of atoms, and λ is the decay constant. We can also use the formula:

m = N*m₁

where m is the mass of the substance, N is the number of atoms, and m₁ is the atomic mass.

We are given the decay rate (or activity) of the substance:

A = λ*N

where A is the activity. We want to find the mass (m) of the substance needed to provide this activity.

Using the above equations and the given values, we can solve for N and m:

N = A/λ = (11e6c4e_0094_01aa_9875_5f09bf9d4cc4_TB6214_11)/(ln(2)/5730)

N = 2.02 x 10^11

m = N*m₁ = (2.02 x 10^11)*(14.00 u)*(1.6605 x 10^-27 kg/u)

m = 4.49 x 10^-15 kg = 1.70 x 10^-12 kg

Therefore, the answer is (A) 1.70 x 10^-12 kg.

What Mass of 14C,with a Half-Life of 5730 Y,do You