Minimum Collision Speed for Excitation of Hydrogen Atoms

In summary, two hydrogen atoms, initially in the ground state, undergo a head on collision with minimum speed required to excite both atoms to the n=2 level. Using the angular momentum equation and the values for mass and radius, the total energy needed can be calculated. When set equal to the kinetic energy of the atoms, the resulting speed is approximately 15,000 m/s. However, previous calculations were incorrect due to a conversion error.
  • #1
cocomisk
3
0

Two hydrogen atoms, both initially in the ground state, undergo a head on collision. If both atoms are to be excited to the n=2 level in this collision, what is the minimum speed each atom can have before the collision?
Ke = 8.99 *10^9
e = 1.602 *10^-19
ħ = 1.05 * 10 ^-34
Mass of electron = 9.11 * 10^-31
mass of proton = .672 * 10^-27



Mass of electron*v*r = nħ This is the angular momentum equation
Total Energy= 1/2 mv^2 - Ke *(e^2 / r)
v^2 = (n^2 * ħ)/(m^2*r^2) = (Ke*e^2)/(m*r)
Radius of n = n^2 * .0529 nm




I can't figure out how to use angular momentum to solve this and that's the only equation my book provides for momentum concerning hydrogen. The closest I have come is using the v^2 equation and using the proton mass rather than the electron mass and using the radius for n=1. This gives me 51043 m/s. The answer is supposed to be 44200 m/s. I assume I need to incorporate the changes in velocity somehow, but I can't figure out how to format an equation to do that.:confused:

Any help is greatly appreciated!


~Courtney
 
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  • #2
I think this is a lot more simple than you're trying to make it. All you need to know is how much energy it takes to get an electron into the n=2 level and then make that equal to the kinetic energy of the atoms and solve for speed. Because the collision is head on you can assume all the energy goes into making the electron jump to the n=2 level.
 
  • #3
E of the ground state = 13.6 eV
E of the n=2 state = 3.4 eV

So the energy required is 10.2 eV or about 6.367 *10^19 J

When I set this equal to 1/2 mv^2, I get a huge number for v...like numbers *10^23. That's incredibly far from the listed answer. What am I doing wrong?
 
  • #4
The energy should be 6.367x10-19 should get a more reasonable answer like 15 000 m/s.
 
  • #5
Yeah I just realized I was converting the numbers wrong.

Thanks Kurdt.
 
  • #6
no problem :smile:
 

Related to Minimum Collision Speed for Excitation of Hydrogen Atoms

1. What is a hydrogen atom collision?

A hydrogen atom collision is a type of interaction between two hydrogen atoms, or between a hydrogen atom and another particle, where the atoms come into contact and their electron clouds interact with each other.

2. How do hydrogen atom collisions occur?

Hydrogen atom collisions can occur through several mechanisms, including thermal collisions, impact ionization, and radiative association. Thermal collisions involve the random movement of particles due to their temperature, while impact ionization is when a high-energy particle collides with a hydrogen atom and removes an electron. Radiative association occurs when two atoms come in close proximity and form a molecule due to the exchange of photons.

3. What are the effects of hydrogen atom collisions?

The effects of hydrogen atom collisions can vary depending on the specific conditions of the collision. In general, they can result in energy transfer, excitation or ionization of the atoms involved, or the formation of new molecules. In extreme cases, collisions can also lead to nuclear fusion, which releases a significant amount of energy.

4. Can hydrogen atom collisions be controlled?

It is difficult to control hydrogen atom collisions due to their random nature. However, scientists can manipulate the conditions in which collisions occur, such as by adjusting temperature or using magnetic fields, to study and understand their effects.

5. What is the significance of studying hydrogen atom collisions?

Studying hydrogen atom collisions can provide valuable insights into the fundamental interactions between particles and the laws of physics. It also has practical applications, such as in plasma physics and astrophysics, and can help us better understand the behavior of matter in extreme environments.

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