Question

Calculate the change in the energy of an electron that moves from the n = 3 level to the n = 2 level. What type of light is emitted?

Answer 1

Red light

Step-by-step explanation:

The energy emitted during an electron transition in an atom of hydrogen is given by

`E=E_0 ((1)/(n_2^2)-(1)/(n_1^2))`

where

`E_0 = 13.6 eV` is the energy of the lowest level

n1 and n2 are the numbers corresponding to the two levels

Here we have

n1 = 3

n2 = 2

So the energy of the emitted photon is

`E=(13.6) ((1)/(2^2)-(1)/(3^2))=1.9 eV`

Converting into Joules,

`E=(1.9 eV)(1.6\cdot 10^(-19) J/eV)=3.0\cdot 10^(-19) J`

And now we can find the wavelength of the emitted photon by using the equation

`E=(hc)/(\lambda)`

where h is the Planck constant and c is the speed of light. Solving for
`\lambda`,

`\lambda=(hc)/(E)=((6.63\cdot 10^(-34))(3\cdot 10^8))/(3.0\cdot 10^(-19))=6.63\cdot 10^(-7) m = 663 nm`

And this wavelength corresponds to red light.