Answer to Question #166900 in Atomic and Nuclear Physics for n

Question

Initially the sample contained 2.0 g of the radioactive isotope. Calculate the number of radioactive nuclei in the sample after 210 seconds.

The number of nuclei in 262 g of dubnium is 6.02 x 10²³

(decay constant: 0.02s-1)

Answer 1

$N = N_0\times e^{-λt} \\ N_0 = 2.0 \;g \\ t = 210 \;s \\ λ = 0.02 \;s^{-1} \\ N = 2.0\times e^{-0.02 \times 210} \\ = 0.0299 \;g$

Proportion:

262 g – $6.02 \times 10^{23}$

0.0299 g – x

$x = \frac{0.0299 \times 6.02 \times 10^{23}}{262} = 6.87 \times 10^{19} \;nuclei$

Answer: $6.87 \times 10^{19} \;nuclei$