An electron that is initially free combines NA proton to for

An electron that is initially free, combines N/A proton to form a hydrogen atom in n=2 state what is the wavelength of the photon emitted in process? Use energy principles. (when the electron is free, the quantum number n is infinity)

Solution

Here,

n = 2

let the wavelength of photon emitted

energy of photon emitted = energy decrease in potential of electron-photon system

h * c/(lamda * e) = 13.6/n^2

6.626 *10^-34 * 3 *10^8/(1.602 *10^-19 * lamda) = 13.6/2^2

solving for lamda

lamda = 3.649 * 10^-7 m

the wavelength of photon emitted in process is 3.649 * 10^-7 m