What is the Orbit of Hydrogen Atom for an Electron at 734 km/s?

In summary, by using Bohr's second postulate and the equation for balancing centripetal and Coulomb forces, we can find the radius of the orbit of an electron moving at 734 km/s in a hydrogen atom. The value for the first Bohr orbit is 0.0529 nm, but for higher values of n, the radius will be larger. Another equation relating r to n or v is needed to find the correct radius.
  • #1
gruba
206
1

Homework Statement


On which orbit of hydrogen atom an electron has the speed of [itex]734 km/s[/itex]?

Homework Equations


Bohr's second postulate: [itex]mvr=nh,m=9.109\cdot 10^{-31}kg,v=734 km/s,h=6.626\cdot 10^{-34} m^{2}kg/s[/itex]

The Attempt at a Solution


By using the second Bohr's postulate, we get [tex]6686.006\cdot 10^{-28}r=6.626\cdot 10^{-34}n[/tex]

Question: What is the value of radius of orbit of electron, [itex]r[/itex]?

If we set that [itex]r=0.0529 nm[/itex], then we get [itex]n=0.053[/itex] and [itex]n[/itex] should be positive integer.
 
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  • #2
gruba said:
If we set that [itex]r=0.0529 nm[/itex]
That value is for the first Bohr orbit, ##n=1##. For ##n > 1##, the radius is bigger. You need another equation relating ##r## to ##n## or ##r## to ##v##.
 
  • #3
DrClaude said:
That value is for the first Bohr orbit, ##n=1##. For ##n > 1##, the radius is bigger. You need another equation relating ##r## to ##n## or ##r## to ##v##.

What is that equation?
 
  • #4
You can use the equation that balances the centripetal force and the Coulomb force. Don't you have that equation in your notes/textbook?
 

Related to What is the Orbit of Hydrogen Atom for an Electron at 734 km/s?

1. What is the orbit of a hydrogen atom?

The orbit of a hydrogen atom refers to the path that the electron follows around the nucleus of the atom. It is often described as being circular, but it is actually more complex and can take on different shapes depending on the energy of the electron.

2. How is the orbit of a hydrogen atom determined?

The orbit of a hydrogen atom is determined by the balance between the attractive force of the positively charged nucleus and the repulsive force of the negatively charged electron. This balance is described by the laws of quantum mechanics.

3. What is the significance of an electron's velocity at 734 km/s in the orbit of a hydrogen atom?

The velocity of an electron in the orbit of a hydrogen atom is significant because it determines the energy level of the electron. The higher the velocity, the higher the energy level, and the further the electron is from the nucleus.

4. How does the orbit of a hydrogen atom change at different velocities?

The orbit of a hydrogen atom changes at different velocities because the energy level of the electron changes. At lower velocities, the electron is closer to the nucleus and has a lower energy level. As the velocity increases, the energy level also increases, causing the electron to move further away from the nucleus.

5. Can the orbit of a hydrogen atom be calculated at a specific velocity?

Yes, the orbit of a hydrogen atom can be calculated at a specific velocity using the Bohr model or the Schrödinger equation. These mathematical models take into account the velocity of the electron and other factors to determine the most likely orbit of the electron around the nucleus.

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