# Electric Current in a Hydrogen Atom

• SuburbanJohn
In summary, the electron orbiting the nucleus at a distance of 5.29 x 10^-11m travels at a speed of 2.19 x 10^6 m/s.
SuburbanJohn
This selection comes from the Serway . Beichner, Physics for Scientists and Engineers text that many undergrads are (I'm sure) familiar with!

I've looked at this problem on 3 different casual occasions and on one test and still have yet to arrange the concept in my mind...

"In the Bohr modle of the hydrogen atom, an electron in the lowest energy state follows a circular path at a distance of 5.29 x 10^-11m from the proton. (a) Show that the speed of the electron is 2.19 x 10^6 m/s (b) What is the effective current associated with this orbiting electron?"

I've been considering the equation $$I_{av} = nqv_{d}A$$, which makes the answer to part (b) a gradeschool word problem. BUT, the answer probably involves implementing some equation derived four chapters ago.

Any hints would be greatly appreciated! Thanks.

John

The equation you need for part (b) is even simpler than that one, since you just have a single charge (an electron) moving at the given speed as it orbits the nucleus.

So, I have a charge 1.602 x 10^-19 C, a distance 5.29 x 10^-11 m, and a value n = 1. I suppose what has me confused is the cross-sectional area.

That formula doesn't apply here. It's meant for situations where you have a charge density with a drift speed. This situation is simpler. How long does it take the electron to make one revolution about the nucleus? I = Q/T.

If I use the velocity given, I calculate 1.52 x 10^-16 sec for one rev. But I 'have' neither the velocity nor the current in part (a).

To solve part (a) you need to review the Bohr model. Given the answer from part (a), you can find the effective current (part (b)). The current (Q/T) is one electron charge per period.

For (b) you derived T, and know Q, so some algebra will give you I.

For (a) my guess would be equate coulombs law to the centripetal force and solve for the velocity.

Doc Al said:
To solve part (a) you need to review the Bohr model.

Ah, so I guess it would have helped to have been taught the Bohr model!

$$F_{e} = k_{e}\frac{q^2}{r^2} = m_{e}\frac{v^2}{r}$$

$$v = [k_{e}\frac{q^2}{rm_{e}}]^\frac{1}{2}$$
$$v = [(8.99 x 10^7)\frac{(1.602 x 10e-19)^2}{(5.29 x 10e-11)(9.10 x 10e-31)}]^\frac{1}{2}$$
$$v = 2,189,240 \frac{m}{s} = 2.19 x 10e6 \frac{m}{s}$$

Golly, that feels gooood! Thanks guys, funny how equations from forever ago come back at ya.. Thanks again!

John

Don't use "x" for multiplication,but either \cdot or \times...

Daniel.

Thanks, I did my best with the scientific notation there. Apparently the ^2 doesn't work when superscripting an integer.

## 1. What is an electric current in a hydrogen atom?

An electric current in a hydrogen atom refers to the flow of charged particles, specifically electrons, within the atom. This current is generated by the movement of electrons from one energy level to another, resulting in the emission or absorption of photons.

## 2. How is electric current produced in a hydrogen atom?

Electric current is produced in a hydrogen atom through the movement of electrons. These electrons can be excited to higher energy levels through the absorption of energy, such as heat or light, and then return to lower energy levels by releasing that energy in the form of photons.

## 3. What is the role of the proton in an electric current in a hydrogen atom?

The proton plays a crucial role in an electric current in a hydrogen atom. It acts as the nucleus of the atom, providing a positive charge that attracts the negatively charged electrons. This attraction allows for the movement of electrons and the generation of an electric current.

## 4. Can electric current in a hydrogen atom be controlled?

Yes, electric current in a hydrogen atom can be controlled by manipulating the energy levels of the electrons. This can be done through the application of external energy, such as through an electrical current or a photon, or by altering the physical properties of the atom, such as its temperature or pressure.

## 5. What are the practical applications of understanding electric current in a hydrogen atom?

Understanding electric current in a hydrogen atom has many practical applications. It is essential in fields such as quantum mechanics, atomic and molecular physics, and spectroscopy. It also plays a crucial role in technologies such as lasers, LED lights, and solar cells.

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