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=1n=1), as shown in the energy-level diagram in the figure (Figure 1). You also observe that it takes a minimum of 17.7 eVeV to ionize this atom.

E1= -17.7

E3= -2.15

What wavelength of photon would be required to induce a transition from the n=1n=1 level to the n=3n=3 level?

Express your answer in nanometers to three significant figures.

Answer 1

E = 0 V

E = - E₁ = 17.7 eV

E₂ = E₁ + hc / e

= - 17.7 + ( 6.627 x 10^-34 x 3 x 10⁸ x / ( 94.54 x 10^-9 x 1.6 x 10^-19 )

= - 4.6 eV

E₃ = E₁ + hc / e

= - 17.7 + ( 6.627 x 10^-34 x 3 x 10⁸ x / ( 79.76 x 10^-9 x 1.6 x 10^-19 )

= - 2.15 eV

E₄ = E₁ + hc / e

= - 17.7 + ( 6.627 x 10^-34 x 3 x 10⁸ x / ( 75.63 x 10^-9 x 1.6 x 10^-19 )

= - 1.3 eV

E₅ = E₁ + hc / e

= - 17.7 + ( 6.627 x 10^-34 x 3 x 10⁸ x / ( 73.86 x 10^-9 x 1.6 x 10^-19 )

= - 0.9 eV

E = E₃ - E₁

= 2.15 - ( - 17.7 )

= 15.55 eV

= h c / e E

= 6.627 x 10^-34 x 3 x 10⁸ / 1.6 x 10^-19 x 15.55

= 7.9907 x 10^-8 m

= 79.907 x 10^-9 m

= 79.907 nm

so the wavelength of photon would be required to induce a transition from the

n=1 level to the n=3 level is = 79.907 nm