I am so stuck on this problem:

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 = 5.

I know 1/lambda = RH (1/n2 - 1/n2)

1/(.4118e-6 m) = RH (1/4 - 1/25)

RH = 1.156e7 ??

Well, well, well, if it isn't the hydrogen spectrum problem! Don't worry, I've got just the clown-tastic answer for you!

You did a great job setting up the equation, but let's check the math together. Ready? Let's dive into the fun zone!

Alright, so we have:

1/λ = RH (1/n1^2 - 1/n2^2)

Plug in the values we know:

1/(.4118e-4 cm) = RH (1/2^2 - 1/5^2)

Now let's do some number juggling:

1/(.4118e-4 cm) = RH (1/4 - 1/25)

To make things easier, let's turn cm into meters: 1 cm = 0.01 m

1/(.4118e-4 m) = RH (1/4 - 1/25)

Now, let's multiply both sides by RH:

RH/(.4118e-4 m) = 1/4 - 1/25

Now for the grand finale, let's simplify everything:

RH = (.4118e-4 m) / (1/4 - 1/25)

All right, drum roll, please... Calculate this and you'll find the RH value! Good luck and keep embracing the wonders of the hydrogen spectrum!

To solve the problem, we can plug in the given values into the Rydberg equation:

1/λ = RH * (1/n1^2 - 1/n2^2)

Given:
λ = 0.4118 x 10^-4 cm
n1 = 2
n2 = 5

First, convert λ to meters:
λ = 0.4118 x 10^-4 cm = 0.4118 x 10^-6 m

Now, substitute the values into the equation:

1/(0.4118 x 10^-6 m) = RH * (1/2^2 - 1/5^2)

Simplifying the equation further:

1/(0.4118 x 10^-6 m) = RH * (1/4 - 1/25)

Now, calculate the RHS (Right Hand Side) of the equation:

1/(0.4118 x 10^-6 m) = RH * ((25 - 4)/(25 * 4))

1/(0.4118 x 10^-6 m) = RH * (21/100)

Now, isolate the RH value:

RH = (1/(0.4118 x 10^-6 m)) * (100/21)

RH ≈ 1.156 x 10^7 m^(-1)

Therefore, the calculated RH value is approximately 1.156 x 10^7 m^(-1).

To solve this problem, you are applying the Rydberg equation, which relates the wavelength of light emitted by an atom to the Rydberg constant (RH) and the principal quantum numbers (n1 and n2). The Rydberg equation is given by:

1/λ = RH (1/n1^2 - 1/n2^2)

In this case, you are given the wavelength (λ) as 0.4118 x 10^-4 cm and you need to calculate the Rydberg constant (RH), given n1 = 2 and n2 = 5.

To begin, convert the given wavelength from cm to meters by dividing by 100:

λ = 0.4118 x 10^-4 cm = 0.4118 x 10^-6 m

Now, substitute the known values into the Rydberg equation:

1/λ = RH (1/n1^2 - 1/n2^2)

1/(0.4118 x 10^-6 m) = RH (1/2^2 - 1/5^2)

Simplify the equation:

1/(0.4118 x 10^-6 m) = RH (1/4 - 1/25)

Now, calculate the value on the left-hand side of the equation:

1/(0.4118 x 10^-6 m) = 2.43056 x 10^6 m^-1

Substitute this value back into the equation:

2.43056 x 10^6 m^-1 = RH (1/4 - 1/25)

To isolate RH, multiply both sides of the equation by the denominator (4-1/25):

2.43056 x 10^6 m^-1 × (4-1/25) = RH

(2.43056 x 10^6 m^-1) × (100/25) = RH

= 9.72224 x 10^6 m^-1 = RH

Therefore, the value of RH is approximately 9.72224 x 10^6 m^-1.

That looks ok to me. The Rydberg constant is 1.097 x 10^7 m^-1 so your calculated value is close.

It's actually 1.097*10nm^-2n^-1