Atomic physics

5)a. Electrons accelerated by a potential difference of 12.23 V pass through a gas of hydrogen atoms at room temperature. Calculate the wavelength of light emitted with the longest possible wavelength.
b. Calculate the wavelength of light emitted with the shortest possible wavelength

For Further Reading

* physics - bobpursley, Sunday, April 13, 2008 at 12:53pm

Energy= 13.6*(1/n^2-1/1^2) which is the energy absorbed in a ground state to n state.
12.23>13.6*(1/n^2-1) or
12.23>13.6/n^2 - 13.6
-13.6/n^2 > -1.11
n^2< 12.34 or max n is 3

Energy= 13.6(1/9-1)=12.08 eV

Now from this, you can calculate max wavelength...

Energy= hf= hc/lambda compute lambda (remember to change eV to joules).



Energy= hf= hc/lambda

lambda=hc/13.2 * n^2)

* physics - Count Iblis, Sunday, April 13, 2008 at 1:06pm

The elctrons have an energy of 12.23 eV. The ionization energy of hydrogen is 13.6 eV. So, the electron beam will create ionized hydrogen as well as hydrogen in excited states.

The shortest wavelength photons are emitted when an 12.23 eV electron from the beam is captured by an ionized hydrogen atom (that atom would then be ionized by an earlier collision with an electron from the beam) and bound in the ground state. The energy of the photon is then 12.23 eV + 13.6 eV = 25.83 eV which corresponds to a wavelength of 48 nm.

There is no upper limit on the wavelength of the photon that can be emitted. When an electron from the beam collides with an hydrogen atom, the bound electron can be kicked out at any energy. These elctrons can be captured by protons at arbitrary high quantum number n. This means that the emitted photon can have arbitrary low energies.

Also, the electrons in the gas will interact with the hydrogen atoms and this will cause emission of photons at arbitrary low energies.

* physics: Correction - Count Iblis, Sunday, April 13, 2008 at 1:10pm

Correction: 12.23 eV is less than the ioniztion energy. So, it is abound state problem as explained by Bobpursley

* physics - Sandhya, Monday, April 14, 2008 at 7:41am

Hello Bobpursley
I don't follow your steps. It is asked about longest & shortest possible wavelengths.Can you please explain?Thanks

Answer this Question

  1. 👍 0
  2. 👎 0
  3. 👁 203
  1. Bob Pursley has shown that the highest value of principle quantum number n that can be excited from the n=1 state by a 12.23 eV electron is n=3. All of the room temperature hydrogen would be in the ground state. It would also be H2, and not H atoms, but the electron beam would dissociate some of the H2.

    The longest wavelngth that would be emitted following an excitation to that level would be the 3-> 2 Balmer line, which is red and at 656.3 nm. Its wavelength can be calulated with the Rydberg formula. The shortest wevelength observable would correspond to the 3-> 1 Lyman series line in the very far "vacuum" ultraviolet, at 102.5 nm. You wold not be able to see this line using a spectrometer that operates in air, because air strongly absorbs the radiation.

    This analysis neglects the possibility of multi-step electronic excitation, which can lead to higher quantum levels and both longer and shorter wavelength emission.

    1. 👍 0
    2. 👎 0
    posted by drwls
  2. Thanks drwls & Bob Pursley for your gerat help.

    1. 👍 0
    2. 👎 0
    posted by Sandhya
  3. Thanks drwls & Bob Pursley for your great help.

    1. 👍 0
    2. 👎 0
    posted by Sandhya

Respond to this Question

First Name

Your Response

Similar Questions

  1. *physics*

    Electrons accelerated by a potential difference of 12.87 V pass through a gas of hydrogen atoms at room temperature. Calculate the wavelength of light emitted with the longest possible wavelength. I don't know what equation to

    asked by Beth Macbeth on March 24, 2008
  2. physics

    The electrons in a TV tube are accelerated from rest through a potential difference of 18kV. Esimate the speed of the electrons after they have been accelerated by this potential difference.

    asked by tony on February 3, 2011
  3. physics

    5)a. Electrons accelerated by a potential difference of 12.23 V pass through a gas of hydrogen atoms at room temperature. Calculate the wavelength of light emitted with the longest possible wavelength. b. Calculate the wavelength

    asked by Sandhya on April 13, 2008
  4. physics - speed of electron in magnetic field

    A beam of electron is accelerated by a potential difference of 2.5okV. The electrons are then allowed to pass into a magnetic field of strength 10.0mT. As the electrons enter the field, the direction of the velocity is at right

    asked by Farah on December 5, 2010
  5. chemistry

    A gas in a discharge tube consists entirely of ions of the same element, of the same charge. Each ion has only one remaining electron. The voltage between the electrodes of the gas discharge tube is increased from zero. Electrons

    asked by schoolgirl on March 23, 2013
  6. Physics

    Electrons are accelerated in the picture tube through a potential difference of 8000 V. What is the change in the potential energy of each electron traveling in this tube? charge of -e is 1.6E-19 C and its mass is 9E-31 kg.

    asked by Mike on February 4, 2008
  7. Physics please help!

    A tungsten target is struck by electrons that have been accelerated from rest through a 38.9-kV potential difference. Find the shortest wavelength of the radiation emitted.

    asked by Gracie on June 7, 2012
  8. physics

    A tungsten target is struck by electrons that have been accelerated from rest through a 24.5-kV potential difference. Find the shortest wavelength of the radiation emitted. (in nm)

    asked by andrej on June 2, 2012
  9. Physics-PLEASE HELP ASAP

    A tungsten target is struck by electrons that have been accelerated from rest through a 38.9-kV potential difference. Find the shortest wavelength of the radiation emitted.

    asked by Kevin on June 7, 2012
  10. Physics

    A tungsten target is struck by electrons that have been accelerated from rest through a 38.9-kV potential difference. Find the shortest wavelength of the radiation emitted.

    asked by Jason on June 7, 2012
  11. Physics Please Help ASAP

    A tungsten target is struck by electrons that have been accelerated from rest through a 38.9-kV potential difference. Find the shortest wavelength of the radiation emitted. (answer has to be in nm)

    asked by Rebecca on June 7, 2012

More Similar Questions