Question

1. suppose each of these isotopes emits an alpha particle. give the isotope name and symbol for the isotope that is produced. place a checkmark next to the isotopes produced that are stable. (consult the isotope graph on page 72 of lesson 14: isotopia.) a. platinum - 175 b. gadolinium - 149 c. americium - 241 d. thorium - 232

Explanation:

Step1: Recall alpha - decay formula

In alpha - decay, the mass number ($A$) of the parent nucleus decreases by 4 and the atomic number ($Z$) decreases by 2. An alpha particle is $_{2}^{4}\text{He}$.

For a parent nucleus $_{Z}^{A}\text{X}$, the decay reaction is $_{Z}^{A}\text{X}
ightarrow_{Z - 2}^{A - 4}\text{Y}+_{2}^{4}\text{He}$.

Step2: Calculate for platinum - 175

Platinum ($\text{Pt}$) has atomic number $Z = 78$. For $_{78}^{175}\text{Pt}$, after alpha - decay, the new atomic number $Z'=78 - 2=76$ and new mass number $A'=175 - 4 = 171$. The element with $Z = 76$ is osmium ($\text{Os}$). So the product is osmium - 171, $_{76}^{171}\text{Os}$.

Step3: Calculate for gadolinium - 149

Gadolinium ($\text{Gd}$) has atomic number $Z = 64$. For $_{64}^{149}\text{Gd}$, after alpha - decay, the new atomic number $Z'=64 - 2 = 62$ and new mass number $A'=149 - 4=145$. The element with $Z = 62$ is samarium ($\text{Sm}$). So the product is samarium - 145, $_{62}^{145}\text{Sm}$.

Step4: Calculate for americium - 241

Americium ($\text{Am}$) has atomic number $Z = 95$. For $_{95}^{241}\text{Am}$, after alpha - decay, the new atomic number $Z'=95 - 2=93$ and new mass number $A'=241 - 4 = 237$. The element with $Z = 93$ is neptunium ($\text{Np}$). So the product is neptunium - 237, $_{93}^{237}\text{Np}$.

Step5: Calculate for thorium - 232

Thorium ($\text{Th}$) has atomic number $Z = 90$. For $_{90}^{232}\text{Th}$, after alpha - decay, the new atomic number $Z'=90 - 2=88$ and new mass number $A'=232 - 4 = 228$. The element with $Z = 88$ is radium ($\text{Ra}$). So the product is radium - 228, $_{88}^{228}\text{Ra}$.

(Note: Without actually consulting the specific isotope graph on page 72, we cannot mark the stable isotopes as required in the problem - statement. But the products of the alpha - decay reactions are calculated as above.)

Answer:

a. Osmium - 171, $_{76}^{171}\text{Os}$
b. Samarium - 145, $_{62}^{145}\text{Sm}$
c. Neptunium - 237, $_{93}^{237}\text{Np}$
d. Radium - 228, $_{88}^{228}\text{Ra}$