Question on absorbtion 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.

 

[rwisz]

Thank you for your question. The absorption spectra of an atom can provide valuable information about its energy levels and can be used to identify the element. In this case, the wavelengths of 97.5 nm and 102.8 nm correspond to specific energy levels in the atom. By using the formula En=-\frac{A}{n^2}, we can calculate the energy difference between these two levels, which will give us the value of A in electron volts.

To do this, we can use the equation E=hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Since we are given the wavelengths, we can plug them into this equation and calculate the energy difference between the two levels. Once we have this value, we can rearrange the formula En=-\frac{A}{n^2} to solve for A.

It is important to note that the value of A will be specific to the element in question. Therefore, we will need to know the atomic number or the element itself in order to determine the value of A in electron volts.

I hope this helps to clarify the use of the absorption spectra and how it can provide information about the atom's energy levels and the value of A.