Answer :
Lead-208 [tex](^{208}_{82}\text{Pb})[/tex] is created through the alpha decay process, where an alpha particle [tex](^4_2\text{He})[/tex] is emitted from a parent isotope. In this case, the parent isotope of Lead-208 is Bismuth-212 [tex](^{212}_{83}\text{Bi})[/tex], as it undergoes alpha decay to produce Lead-208.
An alpha decay reaction can be expressed as:
[tex]^{212}_{83}\text{Bi} \rightarrow ^{208}_{82}\text{Pb} + ^4_2\text{He}[/tex]
To determine the energy released during the decay, we need to consider the difference in mass between the parent isotope and the sum of the masses of the daughter products. This energy is generally released as kinetic energy.
The calculation involves the atomic masses (in atomic mass units, amu) of the isotopes:
- Mass of [tex]^{212}_{83}\text{Bi}[/tex]
- Mass of [tex]^{208}_{82}\text{Pb}[/tex]
- Mass of [tex]^4_2\text{He}[/tex]
The energy released [tex]E[/tex] can be converted from mass to energy using Einstein’s equation, [tex]E=mc^2[/tex], where [tex]c[/tex] is the speed of light [tex]\approx 3.00 \times 10^8\, \text{m/s}[/tex]. After determining the mass difference [tex]\Delta m[/tex] between the initial and final masses, the energy released [tex]E[/tex] in MeV can be calculated using:
[tex]E = \Delta m \times 931.5 \text{ MeV/c}^2[/tex]
Note: The precise atomic masses can be found in nuclear physics tables, and they are needed to perform the exact calculation, including any binding energy effects.
In conclusion, the parent isotope for Lead-208 in alpha decay is Bismuth-212. To calculate the energy released, we use the mass difference between the isotopes and convert it to energy using the mass-energy equivalence principle.
