Question

Ruthenium-106 (106Ru) is used to treat melanoma in the eye. This isotope decays by ?

Answer 1

The atomic number of Ruthenium is 44 and its atomic mass is 106.

Hence Ruthenium is:

The atomic number is equal to the number of protons in the atom.

The atomic mass is the sum of the number of protons and the number of neutrons.

So,

n_p = 44

n_p + n_n = 106

Hence, n_n = 106 - 44 = 62

Ans. No. of protons = 44, No. of neutrons = 62.

If an isotope undergoes beta decay, then it only loses an electron and hence its atomic number does not change. A stable daughter isotope with atomic mass = 106 is Rhodium (¹⁰⁶Rh)

Ans. The missing daughter nucleus is ¹⁰⁶Rh.

Ruthenium undergoes beta decay, which is an exponential decay.

Exponential decay is denoted by the equation

where

N = Present Concentration.

N₀ = Initial Concentration.

= Decay Rate.

t = Time elapsed.

We can also write the equation for time elapsed as

t = -ln(N/N₀)/

The decay rate is related to the half life of the isotope by the relation

= ln2/t_1/2

For ¹⁰⁶Ru, t_1/2 = 373.59 days

= ln2 / 373.59 = 1.86x10^-3 days^-1

We have N/N₀ = 26.5% = 0.265

So

t = -ln(0.265)/1.86x10^-3 = 715.77 days = 715.77 / 365 = 1.96 years

Ans. It takes 1.96 years.