The ionization energy of hydrogen is 1313 kJ/mol. Covert this energy to:

wavelength (nm)

1/wavelength, reciprocal wavelength (cm^-1)

spectral region? (IR, visible, UV, etc.)

I know E=hv=hc/wavelength
h=6.62 x 10^-34 J-s
c= 3x10^8
v=c/wavelength

But for some reason trying to work a problem backwards is confusing me, especially since it's no multiple choice so I can't plug in numbers that way.

1313E3/6.02E23 = ?J/atom = about 2.18E-18 J/atom

E = hc/wavelength
2.18E-18 = 6.626E-34*3E8/wavelength.
Solve for wavelength. I obtained 9.12E-8 m and that x 10^9 for nm.

To convert the ionization energy of hydrogen to wavelength (nm), you can use the equation E = hc/λ. Rearranging the equation to solve for wavelength (λ), you get λ = hc/E.

1. Convert the ionization energy to joules (J):
Ionization energy = 1313 kJ/mol = 1313 x 10^3 J/mol

2. Substitute the values into the equation to find the wavelength:
λ = (6.62 x 10^-34 J-s x 3 x 10^8 m/s) / (1313 x 10^3 J/mol)

λ ≈ 1.514 x 10^-7 m

3. Convert meters to nanometers:
λ = 1.514 x 10^-7 m x 10^9 nm/m

λ ≈ 151.4 nm

Therefore, the ionization energy of hydrogen corresponds to a wavelength of approximately 151.4 nm.

To find the reciprocal wavelength or wave number (cm^-1), you can use the equation:
1/wavelength = ν/c, where ν is the frequency of the light.

1. Calculate the frequency (ν) using the equation ν = c/λ:
ν = 3 x 10^8 m/s / 1.514 x 10^-7 m

ν ≈ 1.982 x 10^15 Hz

2. Convert frequency to reciprocal wavelength or wave number:
1/wavelength = (1.982 x 10^15 Hz) / (3 x 10^10 cm/s)

1/wavelength ≈ 6.607 x 10^4 cm^-1

Therefore, the reciprocal wavelength or wave number is approximately 6.607 x 10^4 cm^-1.

To determine the spectral region, you need to know the range of wavelengths associated with different regions of the electromagnetic spectrum. Here is a general guide:

- Infrared (IR): Wavelengths from about 700 nm to 1 mm.
- Visible: Wavelengths from about 400 nm to 700 nm.
- Ultraviolet (UV): Wavelengths from about 10 nm to 400 nm.

Since the wavelength of approximately 151.4 nm falls within the ultraviolet range, the corresponding spectral region for the given ionization energy of hydrogen is UV.