Question

Radium-226 has a half-life of 1,600 years. How many disintegrations would be measured given in a 1.5 mg sample of Radium-226 per day?

Answer 1

Let, We know;

Rate = N_t x    Where; N_t = No, of atoms of Radium-226

= Decay constant

Now; From the given half-life period t_1/2 =1600 years, We can calculate the Decay constant( ) as;

= 0.693 / t_1/2

=0.693/1600 yr

  = 0.000433 yr^-1

= 0.000433 yr^-1 x ( 1 yr/365 days)

  =1.1866 x 10^-6 day^-1 [As we need our final answer as disintegrations per day]

Now; We have 1.5 mg sample of Radium-226

Converting this 1.5 mg sample to Number of atoms of Radium as;

= 1.5 mg of Ra-226 x ( 1 g/1000mg) x( 1mole/226g)x(6.023x10²³ atoms/1mole)

N_t =3.9976 x10¹⁸ atoms

Now; We know

Rate = N_t x

=3.9976 x10¹⁸ atoms x 1.1866 x 10^-6 day^-1

Rate = 4.7 x10¹² atoms/disintegrations per day