Question

A) By what amount does the mass of a hydrogen atom decrease when its electron makes a down transition from E4 to E1, in an excited hydrogen atom?__kg

B) From what energy level did an electron fall if it emits a photon of 9.38 x10-8 m wavelength when it reaches ground state within a hydrogen atom?

Answer 1

A) The energy levels for the hydrogen atom are given by:

.......EQ1

since electron energy level drops from n1= 4 to n2=1, we get the energy difference as:

.........EQ2

Since this energy is lost and is compensated by decrease in mass in accordance to:

.........EQ3

thus equating EQ2 and EQ3 we get

.......EQ4

we substitute values in EQ4, also 1eV=1.602 x 10^-19 J

B)  We know the wavelength is 9.38 x 10^-8 m. We know energy of the proton is given by:

..EQ5

We know that the electron will lose energy when it drops from n1=n to n2=1. Since lost energy of electron is converted to photon, we omit the negative sign in change in energy,

using EQ2 and EQ 5 we get