λ for one line of the hydrogen spectrum is .4118 x 10-4 cm. Use this value in the Rydberg equation to calculate the RH value using n1 = 2, and n2 = 6.
To calculate the RH value using the given values in the Rydberg equation, we can use the following steps:
Step 1: Write down the Rydberg equation:
1/λ = RH * (1/n1^2 - 1/n2^2)
Step 2: Plug in the given values:
λ = 0.4118 x 10^(-4) cm
n1 = 2
n2 = 6
Step 3: Substitute the values into the equation:
1/(0.4118 x 10^(-4) cm) = RH * (1/2^2 - 1/6^2)
Step 4: Simplify the equation:
1/(0.4118 x 10^(-4) cm) = RH * (1/4 - 1/36)
Step 5: Simplify the fractions:
1/(0.4118 x 10^(-4) cm) = RH * (9/36 - 1/36)
Step 6: Combine the fractions:
1/(0.4118 x 10^(-4) cm) = RH * (8/36)
Step 7: Simplify the fraction:
1/(0.4118 x 10^(-4) cm) = RH * (2/9)
Step 8: Isolate RH by dividing both sides by (2/9):
RH = 1/(0.4118 x 10^(-4) cm) * (9/2)
Step 9: Calculate the RH value:
RH = 9/(2 * 0.4118 x 10^(-4) cm)
Note: Make sure to convert the units appropriately if needed, in this case, cm.
Finally, evaluate the expression:
RH ≈ 1.097 x 10^7 cm^(-1)