NAME: Using Darts to Simulate the Distribution of Electrons in a 1s Orbital Introduction: The quantum theory is based on the mathematical probability of finding an electron in a given three dimensional region of space outside the nucleus of an atom. The region for highest probable e location for an electron is called an orbital. Orbitals can take on various shapes and exist at various distances from the atom s nucleus. In this lab you will drop darts onto a target and then calculate the probability of finding a dart hole at a given distance from the bull s eye of your target. You will then try to relate this to finding an electron in an s orbital of an atom. Materials: Darts, target sheet, large pieces of cardboard measuring about 14 inches by 18 inches (can be cut from cardboard boxes), rulers and masking tape. Safety: Goggles on at ALL times. Conduct yourself in a responsible manner at all times in the laboratory. Procedure: Two or more lab partners should superimpose their target sheets over each other so that when held up to a window, they appear as one sharp target. Carefully tape these targets to a piece of cardboard with two pieces of masking tape. Place the target on the floor with a second piece of cardboard underneath it. With one student standing on a chair with his/her arm held straight out horizontally, a lab partner should adjust the target so that the center of the target is on the floor directly under the other student s extended hand. The student on the chair will then hold his/her hand out horizontally and try to drop the dart onto the bull s eye of the target. The dart should be dropped a total of 100 times. 50 times by one student and 50 times by the lab partner. Basically, one lab partner is dropping the dart 50 times while the other partner is picking it up. It is important that the student dropping the darts waits until his partner is out of the way before dropping a dart. It is very difficult and painful for a teacher to have to explain to a parent why a student is coming home from a chemistry lab with a dart in his/her head. 1
After the dart has been dropped 100 times, separate the target sheets. Each partner should then count the number of holes in sections 1, 2, 3, 4 and 5 of the target. Draw a short line over each hole (with a pencil) as you count the holes. This will ensure that you count each hole only once. If a hole lies directly on a target line, count it towards the inner most region of the target. A hole directly on the line separating the second and third circles of the target should be counted towards the second circle. On the data page, record the number of holes that you counted in each of the five regions of your target. Measure the radius of each concentric circle in the target to the nearest 0.1 cm. Data: Number of holes per ring: Radius of circles: Ring 1: Ring 2: Ring 3: Ring 4: Ring 5: Processing the data: 1.) Calculate the area of each circle from its radius. 2.) Calculate the area of each concentric ring on the target. (Hint): The area of ring 2 = (area of circle 2) (area of circle 1) The area of ring 3 = (area of circle 3) (area of circle 2) etc. 3.) Divide the number of holes in each ring by the area of that ring. Multiply this answer by 10. 2
Area of circles: ( π r 2 ) Circle 1: Circle 2: Circle 3: Circle 4: Circle 5: Area of concentric rings on the target: Ring 1: Ring 2: Ring 3: Ring 4: Ring 5: Holes per unit area x 10: Ring 1: Ring 2: Ring 3: Ring 4: Ring 5: 3
Graph the holes per unit area X 10 against the ring number as shown below (Graph according to instructor s directions). Holes Per Unit Area X 10 Ring Number DATA CHART SUMMARY Ring Number Holes in Ring Area of Ring Holes per Unit Area X 10 1 2 3 4 5 4
QUESTIONS: 1.) Before you started the lab, in what region of the target would you have predicted the most darts would land? Explain. 2.) In doing the experiment, could you predict exactly the precise location where each dart would strike? Explain. 3.) How is this lab similar to how the quantum theory describes the location of an electron? 4.) Using your probability graph, where is the greatest probability of finding an electron in an s orbital? 5.) Where is the lowest probability of finding an s electron? 6.) What is the general shape of the s orbital you created? 7.) What is meant by the statement that s orbitals are non-directional? 8.) What shape does a p orbital take? Draw an example. 9.) Are p orbitals directional? Explain. 10.) Compare your probability graph with an actual scientific graph for finding an s electron. (See the graph below.) 5
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