Solving Quantum Questions with Bohr's Theory

[capslock]

Hi guys, I'm hopelessly stuck on a couple of quantum questions. Any guidance would be very much appreciated!

(1) According to Bohr's theory, what would be the four longest wavelengths of light that can be absorbed by a stationary hydrogen atom initially in its ground state? If an atom absorbs a photon with the longest of these wavelengths, with what velocity does it subsequently move? What is the longest wavelength of light that can ionize such an atom?

(2) A hydrogen atom, initially at rest in the lab frame, in its ground state absorbs a photon with a frequency required to excite it to the first excited state. Calculate the recoil velocity of the atom due to the absorption process and show that the final kinetic energy of the atom is negligible.

James.

 

[Astronuc]

See this reference on the hydrogen spectrum - http://hyperphysics.phy-astr.gsu.edu/Hbase/hyde.html#c4

Transitions to and from the ground state are UV and the series are known as the Lyman series.

Remember - light has momentum p = E/c and the hydrogen atom would have momentum p = mv.

 

[kyle8921]

Hello James,

I am a scientist and I would be happy to help you with your quantum questions. According to Bohr's theory, the four longest wavelengths of light that can be absorbed by a stationary hydrogen atom initially in its ground state are 121.6nm, 102.6nm, 97.3nm, and 94.9nm. If an atom absorbs a photon with the longest wavelength of 121.6nm, it will subsequently move with a velocity of 2.19 x 10^6 m/s. The longest wavelength of light that can ionize such an atom is 91.2nm.

For your second question, the recoil velocity of the hydrogen atom due to the absorption process can be calculated using the formula v = h/λm, where h is Planck's constant, λ is the wavelength of the absorbed photon, and m is the mass of the hydrogen atom. Assuming the absorbed photon has a frequency that is just enough to excite the atom to the first excited state (3.29 x 10^15 Hz), the recoil velocity of the atom would be 6.06 m/s. This is a very small velocity and can be considered negligible.

I hope this helps you with your quantum questions. Let me know if you have any further questions or need clarification on anything. Keep exploring the fascinating world of quantum mechanics!