I'm asked to find the shortest wavelength photon emitted for the paschen series for the hydrogen atom. I used the Rydberg equation and substituted the appropriate values.

Frequency= Rh(1/3^2)-(1/infinity^2)

I get an answer of 820 nm. My online homework program said this answer was wrong, but I feel pretty confident I'm doing this right. What am I doing wrong?

The Rydberg equation is

1/wavelength= R(1/n^2)

1/wavelength=1.097E7(1/9)

wavelength=820.3nm is the shortest.

The equation you used is incorrect for finding the shortest wavelength photon emitted in the Paschen series for the hydrogen atom. The Rydberg equation is used to calculate the wavelengths of photons emitted or absorbed in the hydrogen atom spectrum.

The correct formula for the Rydberg equation is as follows:

1/λ = R_H * (1/n_final^2 - 1/n_initial^2)

Where:
- λ is the wavelength of the photon
- R_H is the Rydberg constant for hydrogen (approximately 1.097 × 10^7 m^-1)
- n_final is the final energy level or principal quantum number
- n_initial is the initial energy level or principal quantum number

To find the shortest wavelength photon in the Paschen series, we need to determine the lowest initial and final energy levels in the series. The Paschen series corresponds to transitions where the electron jumps from higher energy levels to the n=3 energy level.

In this case, the lowest initial energy level (n_initial) would be the n=4 energy level, and the final energy level (n_final) would be the n=3 energy level.

Plug in these values into the Rydberg equation:

1/λ = R_H * (1/3^2 - 1/4^2)

1/λ = R_H * (1/9 - 1/16)

1/λ = R_H * (7/144)

Solve for λ:

λ = 1 / (R_H * 7/144)

λ = 144 / (R_H * 7)

Now, we can substitute the value for the Rydberg constant (R_H ≈ 1.097 × 10^7 m^-1) into the equation:

λ = 144 / (1.097 × 10^7 m^-1 * 7)

λ ≈ 0.0162 m ≈ 16.2 mm

The shortest wavelength photon emitted in the Paschen series for the hydrogen atom is approximately 16.2 mm.

It's possible that your answer of 820 nm is incorrect because you used the wrong values for the initial and final energy levels, or there may have been a calculation error. Double-check your values and calculations, and make sure you're using the correct formula for the Rydberg equation.