Question

¹⁰Be decays by emitting a β^- particle. This decay process has a half-life of 1.52×10⁶ yr. Answer the following questions about this process and report all answers to three significant figures.



1. Determine the initial activity (in dis/yr, do not input units) of a 6.15 mg sample of this isotope. Report your answer to three significant figures in scientific notation.



dis/yr

Tries 0/3

2. Determine the time (in yr) that it takes for the activity of ¹⁰Be to decrease to 4.39×10⁴ dis/yr.

Answer 1

1.

Activity of a sample of radioactive material is given by

Where A = activity

k= disintegration constant

N = number of atoms of the radioactive material

For 10-Be, molar mass = 10.014 g/mol.

1 mol contains avogadro's number of atoms of 10-Be.

Hence, number of atoms present initially in a 6.15 mg sample is

Each atom of 10-Be results in 1 disintegration hence,

Given that the half life =

We can calculate the disintegration constant k as follows

Hence, the initial activity can be calculated as

Hence, your answer should be .

2.

Final activity ,

Since, the nuclear decay follows first order kinetic, we can write

Hence, the time taken for the activity to decrease to the given value is .