Question

PLEASE HELP ME WITH THIS ONE QUESTION

The half-life of Barium-139 is 4.96 x 10^3 seconds. A sample contains 3.21 x 10^17 nuclei. How much of the sample is left after 1.98 x 10^4 seconds?

a) 8.03 x 10^16 nuclei

b) 4.01 x 10^16 nuclei

c) 2.02 x 10^16 nuclei

d) 1.61 x 10^17 nuclei

Answer 1

c) 2.02 x 10^16 nuclei

Step-by-step explanation:

The isotope decay of an atom follows the equation:

ln[A] = -kt + ln[A]₀

Where [A] is the amount of the isotope after time t, k is decay constant, [A]₀ is the initial amount of the isotope

[A] = Our incognite

k is constant decay:

k = ln 2 / Half-life

k = ln 2 / 4.96 x 10^3 s

k = 1.40x10⁻⁴s⁻¹

t is time = 1.98 x 10^4 s

[A]₀ = 3.21 x 10^17 nuclei

ln[A] = -1.40x10⁻⁴s⁻¹*1.98 x 10^4 s + ln[3.21 x 10^17 nuclei]

ln[A] = 37.538

[A] = 2.01x10¹⁶ nuclei remain ≈

c) 2.02 x 10^16 nuclei