- #1

- 7

- 0

**1. Problem:**

The ground-state energy of a hypothetical atom is at -10.0eV. When these atoms, in the ground state, are illuminated with light, only the wavelengths of 207 nanometers and 146 nanometers are absorbed by the light atoms (1 nanometer = 10^-9meters).

**(a)**Calculate the energies of the photons of light of the two absorption-spectrum wavelengths.

**(b)**Complete the energy level diagram shown below for these atoms by showing all the excited energy states.

**(c)**Show by arrows on the energy-level diagram all of the possible transitions that would produce emission-spectrum lines.

**(d)**What would be the wavelength of the emission line corresponding to the transition from the second excited state to the first excited state?

## Homework Equations

E=13.6 [(1/ni^2)-(1/n2^2)]eV

En=-(13.6eV)[(Z^2)/(n^2)]

(1/λ)=(2pi^2mk^2e^4/h^3c)[(1/nf^2)-(1/ni^2)]

2pi^2mk^2e^4/h^3c = 1.097 x 10^7 m

E = hc/λ

hc=1.24 x 10^3eV

## The Attempt at a Solution

**(a)**

207nm = 2.07 x 10^-7m

146nm = 1.46 x 10^-7m

E = hc/λ

E1=[(1.24 x 10^3eV)/(2.07 x 10^-7)]

*E1=5.99 x 10^9*E2=[(1.24 x 10^3eV)/1.46 x 10^-7)]

*E2=8.493 x 10^9***(b)**

I assumed it was bohr model...(?)

Ground state is at -10.0eV

First excited state is 1/4 of ground state

=(1/4)(-10.0eV)

*first excited state=-2.5eV*Second excited state is 1/9 of ground state

=(1/9)(-10.0eV)

*second excited state is -1.11eV*sorry about the terrible picture...

**(c)**is included in picture (?) squiggly arrows..

**(d)**

ni=2

nf=1

(1/λ)=(2pi^2mk^2e^4/h^3c)[(1/nf^2)-(1/ni^2)]

(1/λ)=(1.097 x 10^7 m)[(1/(1)^2)-(1/(2)^2)]

(1/λ)=(1.097 x 10^7 m)[(1/1)-(1/4)]

(1/λ)=(1.097 x 10^7 m)(1-0.25)

(1/λ)=(1.097 x 10^7 m)(0.75)

(1/λ)=8.2275 x 10^6

1=(8.2275 x 10^6)λ

λ=(1/8.2275 x 10^6)

*λ=1.2154 x 10^-7m*