Calculating Energy of Electron in Bohr Hydrogen Atom

[frozen7]

5. The energy En of an electron at the nth orbit in the hydrogen atom is given as:
En = - (13.6 / n2 ) eV where n = 1,2,3, . . . . .
a, If an electron is at n=3, how many spectral transition lines are possible
if it falls to the ground ?


For part a, what does it mean by "how many spectral lines"?

 

[Pengwuino]

If an electron falls from an orbital, it will emit a photon of a certain frequency. This is the "spectral line".

 

[frozen7]

That means the question asking for frequency?

 

[Pengwuino]

No, it is asking how many different photons can be emitted if the electron falls from n=3 to the other possible n-values.

 

[daniel_i_l]

The electron can either fall al at once to the bottom, or it can fall a little at a time. For example it can fall from 3 to 1 generating one line, or from 3 to 2 and then from 2 to 1 giving two different lines. The question asks for the amount of possible different lines.

 

[frozen7]

Then how to determine whether it falls from 3 to 1 or from 3 to 2 and from 2 to 1?

 

[Pengwuino]

Then how to determine whether it falls from 3 to 1 or from 3 to 2 and from 2 to 1?

You don't need to determine what it does, just what is possible for it to do. You've pretty much answered the question, from n=3 to n=1, n=3 to n=2, and n=2 to n=1 all produce different spectral lines because photons with different energies are produced. Thus, 3 different combonations can be produced.

 

[Astronuc]

Read this - http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html

and for more fun and future reference

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/atomstructcon.html#c1

 

[frozen7]

ii. Spectral lines from which spectral series ( Lyman, Balmer etc ) will be seen in the above transition?
iii. State the ionization energy of hydrogen
iv. What is the frequency of light that will ionize hydrogen


This is the following questions related with the question above.

for ii, the answer should be Lyman because it falls to ground state.

for iii, the difference of energy between n = 3 and n = 1 by using
En = - (13.6 / n2 ) eV

for iv, by using the enerygy get from iii, and substitute it into E = hf to find the frequency.

Am I doing correctly?

 

[Astronuc]

For iii, assume that the electron is in its ground state. What energy will ionize it, i.e. what energy is required to remove the electron completely from a bound state around the proton.

For iv, you are correct to use E = h\nu.