What is the probability density at the fifth carbon atom if the electron is in the n=2 energy level?
I have the formula as follows:
Probability density = p5= (2/1.65) sin^2 (4x2pi/11)
I know the final answer is 0.69 nm -1. However, I do not know how to retrieve this final answer using my calculator.. can someone help me please?
I punched it into mine, and it worked.
Is your dRG in radians?
To find the probability density at the fifth carbon atom using the given formula, you will need to use a calculator to evaluate the expression. Here's how you can do it step by step:
1. Start by simplifying the expression inside the sine function:
4 x 2π / 11 ≈ 2.91
2. Next, calculate the sine of the simplified value:
sin(2.91) ≈ 0.225
3. Square the result from step 2 to get the probability density:
0.225^2 ≈ 0.0506
4. Divide the squared value by 1.65:
0.0506 / 1.65 ≈ 0.0307
5. Finally, take the reciprocal of the result from step 4 to obtain the final answer:
1 / 0.0307 ≈ 32.56
Therefore, the probability density at the fifth carbon atom when the electron is in the n=2 energy level is approximately 32.56 nm^(-1).
To retrieve the final answer using your calculator, follow these steps:
1. Enter the value of π (pi) into your calculator. Most calculators will have a π button or you can use an approximate value of 3.14159.
2. Calculate the expression inside the sine function: 4 × 2 × π ÷ 11. This equals approximately 2.283.
3. Calculate the sine of the above value. On most calculators, you can enter the value 2.283, press the sin button, and obtain the result.
4. Square the result from step 3 (sin^2). This will give you the value of sin^2(2.283).
5. Divide the squared value from step 4 by 1.65.
6. Finally, take the result from step 5 and divide it by 0.69 nm^{-1}. The units will cancel out, leaving you with the final answer in nm^{-1}.
Please note that if you are using a scientific calculator, you might need to adjust the order of operations and parentheses accordingly to ensure you obtain the correct result.