Question

Nitrogen 13 has 7 protons and a half life of 600 seconds. What is the activity in Ci after 88.367 minutes? The initial mass of the nitrogen 13 is 93.633 micrograms. The mass of N¹³ is 13.005799 g/mole.

Answer 1

From the given question,

half life(t_1/2)=600 sec

decay constant($\lambda$)=ln (2)/t_1/2

=ln (2)/600

=1.15x 10^-3

N₀=(93.633*10^-6)*6.022*10²³/13.005799

=4.33 x 10¹⁸ atoms

N=N₀e^-$\lambda$t

N=4.33 x 10¹⁸ e^{-(1.15x 10^-3x88.367x60)}

=9.74x 10¹⁵

A=$\lambda$N

=1.15x 10^-3x 9.74x 10¹⁵

=1.12 x 10¹³ Bq

=(1.12 x 10¹³)/(3.7×10¹⁰)

=302.7 Ci

Activity is 302.7 Ci