Question

1. the accepted value for ( r_h ) is ( 1.0974 \times 10^7 , \text{m}^{-1} ). determine the % error using the formula: ( % , \text{error} = \frac{|\text{your answer} - \text{accepted answer}|}{\text{accepted answer}} \times 100 )

Explanation:

To determine the percentage error, we need the "your answer" (the experimental or calculated value of \( R_H \)). Since it's not provided in the question, we can't compute the numerical value of the percentage error. However, here's the step - by - step process assuming we have the "your answer" (let's call it \( y \)):

Step 1: Calculate the absolute difference

First, find the absolute value of the difference between your answer and the accepted answer. The formula for this part is \( |y - 1.0974\times10^{7}\space m^{-1}| \).

Step 2: Divide by the accepted answer

Next, divide the absolute difference obtained in Step 1 by the accepted answer. So we have \( \frac{|y - 1.0974\times10^{7}\space m^{-1}|}{1.0974\times10^{7}\space m^{-1}} \).

Step 3: Multiply by 100 to get the percentage

Finally, multiply the result from Step 2 by 100 to convert it into a percentage. The formula for the percentage error is \( \% \text{Error}=\frac{|y - 1.0974\times10^{7}|}{1.0974\times10^{7}}\times100 \).

If you provide the value of "your answer" (the experimental/calculated \( R_H \)), we can substitute it into the formula and calculate the exact percentage error. For example, if your answer \( y = 1.1\times10^{7}\space m^{-1} \):

Step 1: Calculate the absolute difference

\( |1.1\times 10^{7}- 1.0974\times10^{7}|=|0.0026\times 10^{7}| = 2.6\times10^{4} \)

Step 2: Divide by the accepted answer

\( \frac{2.6\times 10^{4}}{1.0974\times10^{7}}\approx\frac{2.6}{1097.4}\approx0.00237 \)

Step 3: Multiply by 100 to get the percentage

\( 0.00237\times100 = 0.237\% \) (approximate value)

Since the "your answer" is not given in the problem, we can't give a numerical answer for the percentage error. But the formula and the process to calculate it are as above.

Answer:

To determine the percentage error, we need the "your answer" (the experimental or calculated value of \( R_H \)). Since it's not provided in the question, we can't compute the numerical value of the percentage error. However, here's the step - by - step process assuming we have the "your answer" (let's call it \( y \)):

Step 1: Calculate the absolute difference

First, find the absolute value of the difference between your answer and the accepted answer. The formula for this part is \( |y - 1.0974\times10^{7}\space m^{-1}| \).

Step 2: Divide by the accepted answer

Next, divide the absolute difference obtained in Step 1 by the accepted answer. So we have \( \frac{|y - 1.0974\times10^{7}\space m^{-1}|}{1.0974\times10^{7}\space m^{-1}} \).

Step 3: Multiply by 100 to get the percentage

Finally, multiply the result from Step 2 by 100 to convert it into a percentage. The formula for the percentage error is \( \% \text{Error}=\frac{|y - 1.0974\times10^{7}|}{1.0974\times10^{7}}\times100 \).

If you provide the value of "your answer" (the experimental/calculated \( R_H \)), we can substitute it into the formula and calculate the exact percentage error. For example, if your answer \( y = 1.1\times10^{7}\space m^{-1} \):

Step 1: Calculate the absolute difference

\( |1.1\times 10^{7}- 1.0974\times10^{7}|=|0.0026\times 10^{7}| = 2.6\times10^{4} \)

Step 2: Divide by the accepted answer

\( \frac{2.6\times 10^{4}}{1.0974\times10^{7}}\approx\frac{2.6}{1097.4}\approx0.00237 \)

Step 3: Multiply by 100 to get the percentage

\( 0.00237\times100 = 0.237\% \) (approximate value)

Since the "your answer" is not given in the problem, we can't give a numerical answer for the percentage error. But the formula and the process to calculate it are as above.