Question

a) When one atom of iodine-131 decays by beta particle emission, 1.5541 E-13 J are released. The atomic mass of the product nuclide is 130.9051 atomic mass units. Write a nuclear reaction for the decay of iodine-131 and determine its atomic mass in amu. 1 amu = 1.66053886 E -27 kg; mass of a beta particle = 9.10938291 E -31 kg

b) a solution of CuSO4 is measured in a 1.00 cm cuvette and found to have an absorbance of 0.452 units. The molar absorptivity of CuSO4 is 20.6 L/mol*cm. What is the concentration of the solution in M?

Answer 1

1. When one atom of iodine-131(¹³¹I) undergoes beta decay, it releases 1.5541E-13 J of energy. As it is beta decay, the atomic number of the product formed increases by 1, i.e. it forms xenon-131. The reaction is:

The decay energy is the product of the difference in mass of the product and the reactant and the square of the velocity of light, i.e.

Now, the decay energy is given as 1.5541E-13 J with the mass of the product nuclei and electron being 130.9051 amu and 9.10938291E-31 kg.

Taking the mass of I-131 as ‘x’ and using the above formula,

We need to take the mass in the same units, so we need to convert amu to kg.

As we need the mass of I-131 in amu, so the mass is

=130.9066885 amu.

2. The absorbance of CuSO₄ with a path length of 1.00 cm is measured as 0.452 units. The molar extinction coefficient or molar absorptivity is 20.6 L/mol.cm.

As per Beer-Lambert law, absorbance is proportional to the concentration of the solution and path length, i.e.

Where A → absorbance

            ε → molar absorptivity, which is a measure of the probability of electronic transition.

            c → concentration of the solution

            l → path length

Therefore,

  

Therefore, the concentration of CuSO₄ in the solution is 0.0219 M.