Question

1-2

lodine-131 is often used in nuclear medicine to obtain images of the thyroid. If you start with 4.0x10 lodine-131 atoms, how many are left after approximately 1 month? 1-131 has a half- life of 8.0 days. 2) Radium-223 decays with a half-life of 11.4 days. How long will it take for a 0.240-mol sample of radium to decay to 1.50x 10 mol?

Answer 1

Answer – 1) We are given, number of atoms of I-131 = 4.0 *10¹⁰ atoms

time, t = 1 month , half-life t ½ = 8.0 days

First, we need to calculate the decay constant k

we know decay constant , k = 0.693/ t ½

                                             = 0.693/ 8.0 days

                                             = 0.0866 day^-1

now we need to convert time moth to days

we know

1 month = 30.42 days

We know equation for rate of decay

ln [N] / [N_o] = - k * t

We are given initial amount , [N_o] = 4.0 *10¹⁰ atoms

we need to calculate final amount , [N]

ln [N] / 4.0 *10¹⁰ atoms = - 0.0866 day^-1 *30.42 days

ln [N] / 4.0 *10¹⁰ atoms = -2.64

Taking anitln from both side

[N] / 4.0 *10¹⁰ atoms = 0.0717

[N] = 4.0 *10¹⁰ atoms * 0.0717

       = 2.87*10⁹ atoms

so, 2.87*10⁹ atoms of I-131 are left after approximately 1 month.

2) We are given, half-life t ½ = 11.4 days , initial amount [N_o] = 0.240 moles

Final amount [N] = 1.50*10^-2 mol, time = ?

First, we need to calculate the decay constant k

We know decay constant , k = 0.693/ t ½

= 0.693/ 11.4 days

                                              = 0.0608 day^-1

We know equation for rate of decay

ln [N] / [N_o] = - k * t

ln 1.50*10^-2 mol / 0.240 mole = - 0.0608 day^-1 * t

-2.77 = - 0.0608 day^-1 * t

so, t = -2.77 / - 0.0608 day^-1

         = 44.4 days

so, 44.4 days will it take for a 0.240 moles sample of radium to decay to 1.50*10^-2 mol.