Structure of atoms related doubt

Question

Photon is incident have frequency 1×?10?^14 sec^(-1).

Threshold frequency of metal is 5 × ?10?^13 sec^(-1).find kinetic energy of electron 2.electron in hydrogen atom jump from excited state n to ground state.wavelength so emitted Illuminate

Find kinetic energy of electron ?

 

Answer 1

Hi Prashant!

 

It looks like these problems deal with the photoelectric effect (and the Bohr atom in the second part).  Light that illuminates the surface of a metal can eject electrons from the surface, if the light is sufficiently energetic.  The photoelectric effect presents a relationship between the maximum kinetic energy of electrons ejected from the surface of a metal and the energy (and thus, frequency) of the light illuminating the surface, as:

 

KE_max = hf - φ

 

where

 

f = frequency of input light

h = Planck's constant

(and hf is the energy of a photon of the illuminating light)

φ = work function, the minimum energy needed to liberate an electron from the surface

 

The "threshold frequency" of the metal is the frequency of the illuminating light that will just kick an electron off the surface, with no additional kinetic energy.  Thus, when illuminating the metal with the threshold frequency f_t, we have:

 

0 = hf_t - φ -->  hf_t = φ

 

Thus, knowing the threshold frequency allows you to solve for the work function.  Then you can use the full photoelectric effect expression to solve for the maximum kinetic energy (which I assume the first question is asking for) when illuminating with the incident frequency mentioned in the first sentence.

 

For Question 2, we just have to determine the frequency of light emitted from a (Bohr) hydrogen atom when en electron falls from the nth energy level to the ground state (n=1).  The energy lost by such an electron, in electron-volts, is:

 

E = (-13.6 eV)((1/n) - 1)

 

As the electron falls and loses this energy, it emits a photon of equal energy.  The photon energy is related to its frequency by E = hf.

 

So you can calculate the energy of the photon emitted by the electron (in terms of n), and then divide by Planck's constant to get the frequency.  That frequency then goes into the photoelectric effect expression to determine the maximum kinetic energy of electrons kicked off the metal surface when those photons illuminate it.

 

I hope this helps set you on your way.  If you have more questions about this, please let me know.