In a set of experiments on a hypothetical one-electron atom, you measure the wav

Question

In a set of experiments on a hypothetical one-electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground state (n=1), as shown in the energy-level diagram below.(Figure 1) You also observe that it takes 19.1eV to ionize this atom. If the potential energy is taken to be zero for an electron at an infinite distance from the nucleus, find the energy of the atom in the n=4 and n=2 levels shown in the figure, and calculate the wavelength of light emitted when the electron makes a transition from the n=4 to the n=2 level.

a) Find the energy En of the atom in the levels n=2 and n=4 that are shown in the figure.

It is not 32.24eV, 65.46eV. However, the energy of the emitted photons is 15.6eV, 16.42eV.

Explanation / Answer

a.) E2 = 19.1/2^2 = 19.1/4 = 4.775 eV

E4 = 19.1/4^2 = 19.1/16 = 1.19375 eV

b.) E = E2 - E4 = 3.58125 eV

E = hc/lambda

3.58125*1.602x10^-19 = (6.626x10^-34)(3x10^8)/lambda

So wavelength = lambda = 346.5 x 10^-9 m = 346.5 nm

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