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 in the figure (Figure 1) . You also observe that it takes 18.0eV to ionize this atom.

Part A

What is the energy of the atom in each of the levels (n=1,n=2, etc.) shown in the figure?

Answer in the order indicated.

E1=

E2=

E3=

E4=

E5 =

Part B

If an electron made a transition from the n=4 to the n=2 level, what wavelength of light would it emit?

Figure 1 of 1

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 in the figure (Figure 1) . You also observe that it takes 18.0eV to ionize this atom.

Part A

What is the energy of the atom in each of the levels (n=1,n=2, etc.) shown in the figure?

Answer in the order indicated.

E1=

E2=

E3=

E4=

E5 =

Part B

If an electron made a transition from the n=4 to the n=2 level, what wavelength of light would it emit?

Figure 1 of 1

Explanation / Answer

a) Ionization energy = Einfinity - E1 = 0

E1 = - 18.0 eV

E2 = E1 + [hc / lambda e]

= -18.0 + [6.626 * 10-34 * 3 * 108 / 94.54 * 10-9 * 1.602 * 10-19]

E2 = -4.88 eV

E3 = E1 + [hc / lambda e]

= -18.0 + [6.626 * 10-34 * 3 * 108 / 79.76 * 10-9 * 1.602 * 10-19]

E3 = -2.44 eV

E4 = E1 + [hc / lambda e]

= -18.0 + [6.626 * 10-34 * 3 * 108 / 75.63 * 10-9 * 1.602 * 10-19]

E4 = -1.59 eV

E5 = E1 + [hc / lambda e]

= -18.0 + [6.626 * 10-34 * 3 * 108 / 73.86 * 10-9 * 1.602 * 10-19]

E5 = -1.20 eV

--------------------------------------------

delta E = E4 - E2 = -1.59 - (-4.88) = 3.29 eV

lambda = hc / e delta E

= 6.626 * 10-34 * 3 * 108 / (1.6 * 10-19 * 3.29)

= 378 nm

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