how many orbitals are contained in the 2p sublevel? a) 1 b) 2 c) 3 d) 4 question 2 (5 points) how many significant figures should be included in the answer to the following calculation? (3.4876) / (4.11 + 1.2)

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Accepted Answer

### Question 1:
# Brief Explanations:
In atomic structure, p sublevels (regardless of the principal quantum number, like 2p) have 3 orbitals (oriented along x, y, z axes). So the 2p sublevel has 3 orbitals.
# Answer:
c) 3

### Question 2:
# Explanation:
## Step1: Calculate the sum in the denominator
First, calculate $ 4.11 + 1.2 $. $ 4.11 + 1.2 = 5.31 $ (but note significant figures for addition: decimal places matter. 4.11 has two decimal places, 1.2 has one, so result should have one decimal place? Wait, no—for addition, we go by decimal places. 4.11 (two decimal places) + 1.2 (one decimal place) = 5.31, but we round to one decimal place? Wait, no, actually, when adding, the number of decimal places in the result is equal to the least number of decimal places in the terms. 1.2 has one decimal place, 4.11 has two. So $ 4.11 + 1.2 = 5.3 $ (rounded to one decimal place, because 1.2 has one). Wait, no, let's do it properly: 4.11 + 1.2 = 5.31. But since 1.2 has one decimal place, the sum should be reported as 5.3 (one decimal place). Now, for division: $ \frac{3.4876}{5.3} $. The rule for significant figures in division: the result has the same number of significant figures as the least precise measurement. 3.4876 has 5 significant figures, 5.3 has 2 significant figures. Wait, no—wait, the sum: 4.11 (three significant figures, two decimal places) + 1.2 (two significant figures, one decimal place). When adding, the precision is to the tenths place (because 1.2 is precise to tenths). So 4.11 + 1.2 = 5.31, but we round to 5.3 (precise to tenths, so two significant figures? Wait, 5.3 has two significant figures. Then the numerator is 3.4876 (five significant figures). So in division, the number of significant figures is determined by the least number, which is 2? Wait, no, wait: 4.11 is three sig figs, 1.2 is two sig figs. When adding, the result's precision is based on decimal places, not sig figs. 4.11 has two decimal places, 1.2 has one. So the sum should have one decimal place: 5.3 (one decimal place, two sig figs). Then the numerator is 3.4876 (five sig figs). So the division: $ \frac{3.4876}{5.3} $. The denominator has two sig figs, so the result should have two sig figs? Wait, no, wait: 5.3 has two sig figs? Wait, 5.3: the 5 is significant, 3 is significant, so two sig figs. The numerator has five. So the answer should have two sig figs? Wait, no, maybe I messed up. Let's re-express:

First, perform the addition: $ 4.11 + 1.2 = 5.31 $. But when considering significant figures for addition, we look at the number of decimal places. 4.11 has two decimal places, 1.2 has one. So the sum should be rounded to one decimal place: 5.3 (one decimal place). Now, 5.3 has two significant figures (the 5 and 3). The numerator, 3.4876, has five significant figures. When dividing, the result should have the same number of significant figures as the least precise measurement (the one with the fewest sig figs). So 5.3 has two sig figs, so the result should have two sig figs? Wait, no, wait: 5.3 is two sig figs? Wait, 5.3: yes, two. So the answer should have two significant figures? Wait, but let's check again. Wait, 4.11 is three sig figs, 1.2 is two sig figs. When adding, the rule is that the number of decimal places in the sum is equal to the least number of decimal places in the addends. So 4.11 (two decimal places) + 1.2 (one decimal place) = 5.31, which we round to 5.3 (one decimal place). Now, 5.3 has two significant figures. The numerator is 3.4876 (five sig figs). So division: the number of sig figs is determined by the least, which is two. Wait, but maybe I made a mistake. Alternatively, maybe the sum is 5.31 (three sig figs, since 4.11 is three and 1.2 is two, but when adding, sig figs for addition are about decimal places, not total sig figs). So 5.31 has three sig figs? Wait, 5.31: 5, 3, 1—three sig figs. Then the numerator is 3.4876 (five sig figs). Then division: $ \frac{3.4876}{5.31} $. Now, 5.31 has three sig figs, numerator has five. So the result should have three sig figs. Ah, here's the mistake earlier: when adding 4.11 (three sig figs, two decimal places) and 1.2 (two sig figs, one decimal place), the sum is 5.31, which has three sig figs (because the last digit is uncertain? Wait, no, the rule for addition is decimal places. So 4.11 is precise to the hundredth, 1.2 to the tenth. So the sum is precise to the tenth, so we round to the tenth: 5.3 (one decimal place), which is two sig figs. But wait, 5.3 is two sig figs, 5.31 is three. Which is correct? Let's recall: the number of decimal places in the sum is equal to the least number of decimal places in the addends. So 4.11 has two decimal places, 1.2 has one. So the sum should have one decimal place: 5.3 (one decimal place), which is two sig figs. Therefore, the denominator is 5.3 (two sig figs), numerator is 3.4876 (five sig figs). So the division result should have two sig figs. Wait, but maybe the question is about the intermediate step? Wait, no, the question is "How many significant figures should be included in the answer to the following calculation? (3.4876)/(4.11 + 1.2)". So first, calculate the denominator: 4.11 + 1.2. Let's do this without rounding first: 4.11 + 1.2 = 5.31. Now, for significant figures in addition, the precision is to the tenths place (because 1.2 is to the tenths), so the sum is 5.3 (to the tenths place), which has two significant figures. Then, the numerator is 3.4876 (five significant figures). When dividing, the number of significant figures is determined by the least number, which is two. Wait, but maybe the problem is considering the sum as 5.31 (three significant figures) because 4.11 is three and 1.2 is two, but when adding, the rule is decimal places, not total sig figs. So this is a bit confusing. Alternatively, maybe the intended approach is:

1. Calculate the denominator: 4.11 + 1.2 = 5.31. Now, 4.11 has three significant figures, 1.2 has two. When adding, the result's number of decimal places is equal to the least number of decimal places in the addends. 4.11 has two decimal places, 1.2 has one. So we round the sum to one decimal place: 5.3 (one decimal place), which has two significant figures.

2. Now, the numerator is 3.4876 (five significant figures). When dividing, the result should have the same number of significant figures as the least precise measurement (the one with the fewest sig figs). So 5.3 has two sig figs, so the answer should have two sig figs. Wait, but maybe the problem is considering the sum as 5.31 (three sig figs) because 4.11 is three and 1.2 is two, but that's incorrect. The rule for addition is decimal places, not total sig figs. So the correct number of significant figures in the answer should be two? Wait, no, let's check a reference. For addition/subtraction, the result has the same number of decimal places as the term with the least number of decimal places. For multiplication/division, the result has the same number of significant figures as the term with the least number of significant figures.

So in this case:

- First, perform the addition in the denominator: 4.11 (two decimal places) + 1.2 (one decimal place) = 5.31. We round this to one decimal place: 5.3 (one decimal place). Now, 5.3 has two significant figures (the 5 and 3).

- Then, perform the division: 3.4876 (five significant figures) ÷ 5.3 (two significant figures). The result should have two significant figures.

Wait, but maybe the problem is not rounding the intermediate step? Let's see: 4.11 + 1.2 = 5.31 (exact sum, no rounding yet). Now, 5.31 has three significant figures (5, 3, 1). The numerator has five. So when dividing, we take the least number of significant figures, which is three (from 5.31). Therefore, the answer should have three significant figures. Ah, this is the key: when doing calculations, we don't round intermediate steps. We keep extra digits during calculation and round only at the end. So:

1. Calculate the denominator: 4.11 + 1.2 = 5.31 (this is the exact sum, no rounding). Now, 5.31 has three significant figures (since 4.11 has three and 1.2 has two, but when adding, we don't round intermediate steps; we just note the precision for the final answer).

2. Now, the numerator is 3.4876 (five significant figures).

3. For the division $ \frac{3.4876}{5.31} $, the number of significant figures is determined by the least number, which is three (from 5.31).

Therefore, the answer should have three significant figures.

# Answer:
3 (assuming the correct approach is not rounding intermediate steps, so the denominator has three sig figs, leading to three sig figs in the answer)

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Explanation:

Question 1:

Step1: Calculate the sum in the denominator

Answer:

Question 2: