Questions About Ruthenium 106 and Brachytherapy

[mandy9008]

Homework Statement

1. Ruthenium 106 is used in brachytherapy. It has a half-life of 1.02 years. Ruthenium 106 decays by beta emission (e-) to rhodium 106. The mass of ruthenium 106 is 105.907330 u and the mass of rhodium 106 is 105.907288 u. Rhodium 106 is not a stable isotope of rhodium. Consider a microgram of ruthenium 106 inserted into the body for therapy.

How many atoms of ruthenium are in a microgram of ruthenium 106?

After 1.02 years have passed, how many micrograms of ruthenium are present in the body?

After 0.90 years have passed, how many micrograms of ruthenium are present in the body?

After six half lives have passed, how many ruthenium atoms are still present in the body from the therapy?

Write out the equation representing the beta decay (e-) of ruthenium 106.

If the electron comes off with 0.0354 MeV of energy, determine the energy of the antineutrino.

Why is it important in brachytherapy to realize that rhodium is not a stable isotope?
If rhodium were not a stable isotope what considerations must one make?

I have answered/solved most of these questions, but I am not 100% sure that they are right.

Homework Equations

N(t) = N_o e ^-t/t_1/2

The Attempt at a Solution

How many atoms of ruthenium are in a microgram of ruthenium 106?
1 microgram = 10^-6 g
10^-6g ((6.022 x 10²³ atoms/mol) / (106 g/mol)) = 5.68 x 10¹⁵ atoms

After 1.02 years have passed, how many micrograms of ruthenium are present in the body?
N(t) = N_o e ^-t/t_1/2
N_o = 5.68 x 10¹⁵ atoms
t=1.02 yrs
t_1/2=1.02 yrs

5.68 x 10¹⁵ atoms e^(-1.02/1.02) = 2.09 x 10¹⁵ atoms

2.09 x 10¹⁵ atoms (106 g/mol / (6.022 x 10²³ atoms/mol)) = 3.68 x 10^-7g = 0.368 micrograms

After 0.90 years have passed, how many micrograms of ruthenium are present in the body?

N(t) = N_o e ^-t/t_1/2
N_o = 5.68 x 10¹⁵ atoms
t=0.09 yrs
t_1/2=1.02 yrs

5.68 x 10¹⁵ atoms e^(-0.09/1.02) = 5.20 x 10¹⁵ atoms

5.20 x 10¹⁵ atoms (106 g/mol / (6.022 x 10²³ atoms/mol)) = 9.15 x 10^-7g = 0.915 micrograms

After six half lives have passed, how many ruthenium atoms are still present in the body from the therapy?
To find the six half lives, I divided the half life, 1.02 yrs, by 2, 6 times, giving me 0.00796875 yrs

5.68 x 10¹⁵ atoms e^{(-0.00796875/1.02)} = 5.64 x 10¹⁵ atoms

Write out the equation representing the beta decay (e-) of ruthenium 106.
I am not sure what equation this is asking for. My guess would be for the Q factor..
Q=(mass of reactants-mass of products) c²
Q=(105.907330u - 105.907288u)c²

If the electron comes off with 0.0354 MeV of energy, determine the energy of the antineutrino.
I am not sure on this one. Could someone help me to get started, please?

Why is it important in brachytherapy to realize that rhodium is not a stable isotope?
If rhodium were not a stable isotope what considerations must one make?
I am not really sure why a stable isotope would be necessary for this.

 

[phyzguy]

You're missing a factor in the exponent. If the half-life is 1.02 years, then after 1.02 years half of the original amount will have decayed - that's why it's called a half-life. I suggest you go back and review the relation between the half-life and the exponential decay constant (usually called lambda).