Question

each of the following sets of quantum numbers is supposed to specify an orbital. choose the one set of quantum numbers that does not contain an error. a n = 2, l = 2, ml =+1 b n = 2, l = -1, ml =0 c n = 3, l = 2, ml =+3 d n = 4, l = 3, ml =-2 question 8 10 points a student performs an experiment to determine the density of a sugar solution. she obtains the following results: 1.71 g/ml, 1.73 g/ml, 1.67 g/ml, 1.69 g/ml. if the actual value for the density of the sugar solution is 1.40 g/ml, which statement below best describes her results? a her results are neither precise nor accurate. b her results are precise, but not accurate. c her results are accurate, but not precise. d her results are both precise and accurate

Explanation:

Step1: Recall quantum - number rules

The principal quantum number \(n\) can take values \(n = 1,2,3,\cdots\). The angular - momentum quantum number \(l\) can take values \(l=0,1,\cdots,n - 1\). The magnetic quantum number \(m_l\) can take values \(m_l=-l,-l + 1,\cdots,0,\cdots,l-1,l\).

Step2: Analyze option A

For \(n = 2\), \(l\) can be \(0\) or \(1\). Since \(l = 2\) in option A, it is incorrect.

Step3: Analyze option B

The value of \(l\) cannot be negative. Since \(l=-1\) in option B, it is incorrect.

Step4: Analyze option C

For \(l = 2\), \(m_l\) can range from \(-2\) to \(2\). Since \(m_l = 3\) in option C, it is incorrect.

Step5: Analyze option D

For \(n = 4\), \(l\) can be \(0,1,2,3\). For \(l = 3\), \(m_l\) can be \(-3,-2,-1,0,1,2,3\). So \(n = 4\), \(l = 3\), \(m_l=-2\) is a valid set of quantum numbers.

Step6: Recall precision and accuracy concepts

Precision refers to the closeness of a set of measurements to each other. Accuracy refers to the closeness of a measurement to the true value.

Step7: Analyze the density - measurement results

The measured values \(1.71\ g/mL\), \(1.73\ g/mL\), \(1.67\ g/mL\), \(1.69\ g/mL\) are close to each other, so they are precise. But they are all significantly higher than the actual value of \(1.40\ g/mL\), so they are not accurate.

Answer:

D. \(n = 4\), \(l = 3\), \(m_l=-2\)
B. Her results are precise, but not accurate.