4. Naturally occurring palladium (Pd) has six isotopes. Palladium-103 is a radio

Question

4. Naturally occurring palladium (Pd) has six isotopes. Palladium-103 is a radioisotope which has uses in radiation therapy for treating prostate cancer. It decays by electron capture, and also emits gamma rays by doing so. (a) Write a balanced nuclear equation for this decay process: (b) Calculate the binding energy per nucleon for the Palladium-103 isotope, which has a mass of 102.906087 amu. Express your answer in MeV/nucleon. Given: 1 neutron = 1.008665 amu; 1 proton = 1.007276 amu; mass/energy conversion = 931.5 MeV/amu (c) The half-life of Palladium-103 is 17 days. How many days would it take for 16 g to decay to 1.0 g?

Explanation / Answer

A)   Pd-103 + e- --> Rh-103 (p+ + e- --> n; mass unchanged)

b) A Palladium-103 nucleus contains 46 protons and 60 neutrons.

The total mass = 46 x (1.007276 amu) + 60 x (1.008665 amu) = 106.85 amu

The actual mass of Pd-103 = 102.906087 amu

The mass defect = 106.85 amu - 102.906087 amu = 3.9485 amu

Binding Energy = 3.9485 amu x 931.5 MeV/amu = 3678.04 MeV

Binding energy per nucelon = 3678.04 / 103 = 35.71 MeV/nucleon

B) Binding energy per nucleon for the Palladium-103 = 35.71 MeV/nucleon

C)

Following one half-life, you have 8g

After 2 half-lifes = 4g

3 half-lifes = 2g

4 half-lifes = 1g

(4 x 17) = 1.0g Pd-103

C) Number of days for Pd-103 to decay to 1.0g = 68 days

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