Finding Kinetic Energy of an Electron in a Hydrogen Atom and a Cathode Ray Tube

In summary, to find the kinetic energy of an electron in the lowest allowed energy state of a hydrogen atom, you can use the equation E = (mv^2)/2 = (mq^4)/(2(4pi*epsilon_0)^2*n^2*hbar^2), where m is the mass of the electron, q is the charge, n is the principal quantum number, and hbar is the reduced Planck's constant. For the second problem, to relate kinetic energy and potential, you can use the equation E = (mv^2)/2 = (mq^4)/(2(4pi*epsilon_0)^2*n^2*hbar^2), where E is the total energy, m is
  • #1
user101
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Homework Statement



Find the kinetic energy of an electron in the lowest allowed energy state of a hydrogen atom.

Homework Equations



[tex]E = \frac{mv^2}{2} = \frac{mq^4}{2(4\pi\epsilon_0)^2n^2\hbar^2}[/tex]

The Attempt at a Solution



m = 9.11* 10^(-31) kg
q = 1.6 * 10^(-19) C
pi = 3.14
n = 1
hbar = 6.59 * 10^(-16) eV * s

Are the values I chose correct?
Next Problem:

Homework Statement



Find the kinetic energy of a free electron, initially at rest at the back of a cathode ray tube, accelerated through a potential of 10kV to strike the phosphor layer.

Homework Equations



[tex]E = \frac{mv^2}{2} = \frac{mq^4}{2(4\pi\epsilon_0)^2n^2\hbar^2}[/tex]

The Attempt at a Solution



I'm not too sure how to relate KE and potential.

I know that Total Energy = Potential E + Kinetic E, but I don't know Total Energy in order to use that generalized equation.

The next thing I thought was to use [tex]Epotential = Evacuum - \frac{q^2}{4\pi\epislon_0r}[/tex], but wasn't sure how to take into account the 10kV. Any help?
 
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  • #2
For the second question, the kinetic energy gained by an electron passing through 1 volt of electrostatic potential is 1 eV, so a 10kV potential would yield an increase in kinetic energy of 10keV, right? What is the energy of the free electron before being accelerated through the potential?
 
  • #3
EricVT said:
For the second question, the kinetic energy gained by an electron passing through 1 volt of electrostatic potential is 1 eV, so a 10kV potential would yield an increase in kinetic energy of 10keV, right? What is the energy of the free electron before being accelerated through the potential?

Well, for the electron BEFORE being accelerated would have no KE value. So, this would mean that the only KE gain would be the 10keV you described above?
 

1. What is the formula for calculating the kinetic energy of an electron in a hydrogen atom?

The formula for calculating the kinetic energy of an electron in a hydrogen atom is: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the electron, and v is the velocity of the electron.

2. How is the kinetic energy of an electron in a hydrogen atom related to its orbital radius?

The kinetic energy of an electron in a hydrogen atom is inversely proportional to its orbital radius. This means that as the electron's orbital radius increases, its kinetic energy decreases, and vice versa.

3. What is the significance of finding the kinetic energy of an electron in a cathode ray tube?

The kinetic energy of an electron in a cathode ray tube is important because it helps us understand the behavior and movement of electrons in a vacuum. It also allows us to calculate the acceleration and velocity of the electrons, which is crucial for the functioning of the cathode ray tube.

4. How does the kinetic energy of an electron in a hydrogen atom differ from that of an electron in a cathode ray tube?

The kinetic energy of an electron in a hydrogen atom is a result of its orbital motion around the nucleus, while the kinetic energy of an electron in a cathode ray tube is a result of its acceleration by an electric field. Additionally, the magnitude of the kinetic energy in a hydrogen atom is much smaller compared to that in a cathode ray tube due to the higher velocities and accelerations involved in the latter.

5. Can the kinetic energy of an electron in a hydrogen atom or cathode ray tube be changed?

Yes, the kinetic energy of an electron in a hydrogen atom or cathode ray tube can be changed by altering its velocity or acceleration. This can be done by changing the electric field strength or by colliding the electron with other particles or objects. In a hydrogen atom, the kinetic energy can also be changed by changing the electron's orbital radius.

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