Question

a) Find the energy of an electron in the n=5 state of the hydrogen atom. 

b) Find the energy of an electron in the n=6 state of the hydrogen atom. 

c) If an electron initially in the n= 6 state falls to the n= 5 state, how much energy must the electron give up? 

d) If an electron initially in the n= 6 state falls to the n=5 state, what is the wavelength of the photon that will be emitted?

Answer 1

Energy of electron in in hydrogen atom is given by:

  

Where, n is no of orbit/state in which electron is present.

Z is the atomic number , for hydrogen atom Z=1

a). Now energy of electron in n= 5 state is

  

b).Now energy of electron in n=6 orbit /state is:

  

c). As we have shown n=6 has higher energy (less negative value ) than n=5 so when electron jumps from n=6 to n=5 energy will release in form of photons

Energy released = difference in energy of n=6. and  n=5 orbit/state .

  

d).Energy of photon

Where h : planck's constant

c: speed of light in vacuum

: wavelength of emitted light

Now

So

Wavelength of emitted photon is