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**1. Homework Statement**

The emission spectrum of an unknown substance contains lines with the wavelengths 172 nm, 194 nm , and 258 nm, all resulting from transitions to the ground state.

a) Calculate the energies of the first three excited states.

b) Calculate the wavelengths of three other lines in the substance's emission spectrum.

**2. Homework Equations**

E = hc/ wavelength

wavelength 1 = 2.58x10^-7 m

wavelength 2 = 1.94x10^-7 m

wavelength 3 = 1.72x10^-7 m

**3. The Attempt at a Solution**

a) First Energy level : E = ((6.63x10^-34)(3.00x10^8)) / (2.58x10^-7) = 7.71 x10^-19 J

Convert to eV: 7.71x10^-19 J / 1.6x10^-19 J/eV = 4.82 eV

Second Energy level : E=((6.63x10^-34)(3.00x10^8)) / (1.94x10^-7) = 1.025x10^-18 J

Concert to eV: 1.025x10^-18 J / 1.6x10^-19 J/eV = 6.41 eV

Third Energy level: E = ((6.63x10^-34)(3.00x10^8)) / (1.72x10^-7) = 1.1564x10^-18 J

Concert to eV: 1.1564x10^-18 J / 1.6x10^-19 = 7.22 eV

b) lamda = hc/Ef-Ei

I know it has something to do with subtracting with the 3 energy levels from above to figure out the three new lamdas but that didn't turn out properly.

the answers are: 518nm,782m, and 152 nm.

If anyone could point me to the right direction, I'd be greatly appreciated.