How Can Wavelengths Help Determine the Constant A in Absorption Spectra?

[semc]

An atom has energy levels E_n=-$$\frac{A}{n^2}$$ where n is an integer and A is a constant.
Among the spectral lines that the atom can absorb at room temperature are two
adjacent lines with wavelengths 97.5 nm and 102.8 nm. Find the value of the constant
A in electron volts.

Initially I thought we can equate the coulomb force to the centripetal force but we are not told the atomic number or atom. Totally no clue, how is the wavelength useful when you do not know what atom it is?

 

[rl.bhat]

Energy of the photon absorbed or emitted is given by

$$E_n = \frac{hc}{\lambda} = A(1 - \frac{1}{n^2})$$

Smaller wave length will have larger energy.

Write down two equations for two wavelength and solve them to find A and n.

 

[semc]

We can assume transition from n quantum state to n=1?

 

[rl.bhat]

Since the spectral lines that the atom can absorb at room temperature are two
adjacent lines with wavelengths 97.5 nm and 102.8 nm, you have to find energies of
$$E_n and E_{n+1}$$ with respect to the ground state.