Questions: Question #13: Objective 3.3 Calcium (20Ca) has 26 known isotopes, ranging from 35Ca to 60Ca. Using 5 of those isotopes: 35Ca, 40Ca, 41Ca, 42Ca, 52Ca Two of those listed above are stable and three are radioactive. Explain which isotopes you believe are stable and why, and which isotopes you believe are radioactive and why. (answering the why is the important part) Need at least 2 different reasons why. You don't need to state what radiation they will release (so the answer to this question will not be found looking up these isotopes on Wikipedia or the dynamic periodic table) Answer the above question in your Knowledge Check Answer Sheet Page 4 (make sure you include the symbol Ca in your explanation)

Question #13: Objective 3.3 Calcium (20Ca) has 26 known isotopes, ranging from 35Ca to 60Ca.

Using 5 of those isotopes: 35Ca, 40Ca, 41Ca, 42Ca, 52Ca Two of those listed above are stable and three are radioactive. Explain which isotopes you believe are stable and why, and which isotopes you believe are radioactive and why. (answering the why is the important part) Need at least 2 different reasons why. You don't need to state what radiation they will release (so the answer to this question will not be found looking up these isotopes on Wikipedia or the dynamic periodic table) Answer the above question in your Knowledge Check Answer Sheet Page 4 (make sure you include the symbol Ca in your explanation)

Transcript text: Question #13: Objective 3.3 (unbolded objective) Calcium (20Ca) has 26 known isotopes, ranging from ${ }^{35} \mathrm{Ca}$ to ${ }^{60} \mathrm{Ca}$. Using 5 of those isotopes: ${ }^{35} \mathrm{Ca},{ }^{40} \mathrm{Ca},{ }^{41} \mathrm{Ca},{ }^{42} \mathrm{Ca},{ }^{52} \mathrm{Ca}$ Two of those listed above are stable are three are radioactive. Explain which isotopes you believe are stable and why, and which isotopes you believe are radioactive and why. (answering the why is the important part) Need at least 2 different reasons why You don't need to state what radiation they will release (so the answer to this question will not be found looking up these isotopes on wikipedia or the dynamic periodic table) answer the above question in your Knowledge Check Answer Sheet Page 4 (make sure you include the symbol Ca in your explanation)

Solution

Solution Steps

Step 1: Understanding Isotopes and Stability

Isotopes of an element have the same number of protons but different numbers of neutrons. The stability of an isotope is influenced by the ratio of neutrons to protons (N/Z ratio) and the overall nuclear binding energy. Generally, isotopes with a balanced N/Z ratio and higher binding energy per nucleon are more stable.

Step 2: Identifying Stable Isotopes

For calcium (Ca), the most common and stable isotopes are those with a balanced N/Z ratio. Typically, elements with atomic numbers less than 20 have stable isotopes when the N/Z ratio is close to 1. For calcium, which has 20 protons, the stable isotopes are usually those with around 20 neutrons.

Step 3: Analyzing Given Isotopes

$^{35}\text{Ca}$: This isotope has 15 neutrons and 20 protons, giving an N/Z ratio of 0.75, which is significantly lower than 1. This suggests instability.
$^{40}\text{Ca}$: This isotope has 20 neutrons and 20 protons, giving an N/Z ratio of 1. This balanced ratio suggests stability.
$^{41}\text{Ca}$: This isotope has 21 neutrons and 20 protons, giving an N/Z ratio of 1.05, which is close to 1, suggesting potential stability.
$^{42}\text{Ca}$: This isotope has 22 neutrons and 20 protons, giving an N/Z ratio of 1.1, which is slightly higher but still close to 1, suggesting potential stability.
$^{52}\text{Ca}$: This isotope has 32 neutrons and 20 protons, giving an N/Z ratio of 1.6, which is much higher than 1, indicating instability.

Step 4: Conclusion on Stability

Based on the N/Z ratio and general nuclear stability principles:

Stable Isotopes: $^{40}\text{Ca}$ and $^{42}\text{Ca}$ are likely stable due to their balanced N/Z ratios.
Radioactive Isotopes: $^{35}\text{Ca}$, $^{41}\text{Ca}$, and $^{52}\text{Ca}$ are likely radioactive due to their unbalanced N/Z ratios, with $^{35}\text{Ca}$ and $^{52}\text{Ca}$ being more extreme cases.