Velocity of Electron ionized from Hydrogen

In summary, the question asks for the kinetic energy of electrons that are freed when ultraviolet light with a wavelength of 45.0nm shines on a gas of hydrogen atoms in their ground states. The equation used to solve for kinetic energy is k=0.5mv^2, with a given mass of 9.11x10^-31 kg and an energy of 14eV. The attempted solution involves finding the velocity using v=√(2k/m), but it is important to remember to use units of eV0.5kg-0.5 instead of m/s. Writing down the units can help avoid errors in the calculation.
  • #1
DRC12
41
0

Homework Statement


Ultraviolet light with a wavelength of 45.0nm shines on a gas of hydrogen atoms in their ground states. Some of the atoms are ionized by the light. What is the kinetic energy of the electrons that are freed in this process?
I found the kinetic energy right but for some reason I thought I was looking velocity and when I solve for velocity I get a number much larger then the speed of light

Homework Equations


k=.5mv2
k=14eV
m=9.11*10-31kg

The Attempt at a Solution


k=.5mv2
v2=2k/m
v=√(2*14/9.11*10-31)=5.54*1015m/s
am I doing something wrong or is there some quantum equation needed
 
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  • #2
DRC12 said:

Homework Statement


Ultraviolet light with a wavelength of 45.0nm shines on a gas of hydrogen atoms in their ground states. Some of the atoms are ionized by the light. What is the kinetic energy of the electrons that are freed in this process?
I found the kinetic energy right but for some reason I thought I was looking velocity and when I solve for velocity I get a number much larger then the speed of light

Homework Equations


k=.5mv2
k=14eV
m=9.11*10-31kg

The Attempt at a Solution


k=.5mv2
v2=2k/m
v=√(2*14/9.11*10-31)=5.54*1015m/s
am I doing something wrong or is there some quantum equation needed

Find the kinetic energy in joules, and calculate the speed with that value. Now you have the speed in units of eV0.5kg-0.5 instead of m/s.

ehild
 
  • #3
Oh, thanks, I keep forgetting about that. I really need to start writing down the units
 
  • #4
DRC12 said:
Oh, thanks, I keep forgetting about that. I really need to start writing down the units

It is a good idea !:smile:

ehild
 
  • #5


I would like to clarify that the velocity of an electron cannot be directly determined from its kinetic energy. The relationship between kinetic energy and velocity is given by the equation K = 1/2 mv^2, where K is the kinetic energy, m is the mass of the electron, and v is its velocity. However, this equation only holds for classical mechanics and does not take into account quantum effects.

In the case of an electron being ionized from a hydrogen atom, the kinetic energy of the electron can be calculated using the equation K = 13.6 eV - E, where E is the energy of the photon that ionized the electron. In this case, E can be calculated using the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the ultraviolet light.

So, to find the kinetic energy of the electron, we can use the equation K = 13.6 eV - hc/λ. Plugging in the values given in the problem, we get K = 13.6 eV - (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/(45.0 x 10^-9 m) = 13.6 eV - 0.442 eV = 13.158 eV.

Therefore, the kinetic energy of the electron is 13.158 eV. However, as mentioned earlier, this does not directly give us the velocity of the electron. To find the velocity, we would need to use quantum equations and take into account the wave-particle duality of electrons. So, the velocity of the electron cannot be determined from the given information.
 

What is the velocity of an electron ionized from hydrogen?

The velocity of an electron ionized from hydrogen can vary depending on several factors such as the energy of the photon that ionized it, the direction of emission, and the presence of external electric or magnetic fields. However, on average, the velocity of an electron ionized from hydrogen is approximately 2.18 million meters per second.

How is the velocity of an electron ionized from hydrogen calculated?

The velocity of an electron ionized from hydrogen can be calculated using the equation v = (2E/m)^1/2, where v is the velocity, E is the energy of the photon, and m is the mass of the electron. This equation is based on the conservation of energy and momentum.

What factors affect the velocity of an electron ionized from hydrogen?

The velocity of an electron ionized from hydrogen can be affected by several factors, such as the energy of the photon that ionized it, the direction of emission, the presence of external electric or magnetic fields, and the interactions with other particles in its environment.

Why is the velocity of an electron ionized from hydrogen important?

The velocity of an electron ionized from hydrogen is important because it can provide valuable information about the energy and interactions of the electron. It is also a fundamental aspect of understanding the behavior of atoms and molecules, as well as various processes in astrophysics and plasma physics.

How does the velocity of an electron ionized from hydrogen relate to its energy?

The velocity of an electron ionized from hydrogen is directly related to its energy. This is because the kinetic energy of an electron is given by the equation KE = 1/2mv^2, where m is the mass of the electron and v is its velocity. As the velocity increases, so does the kinetic energy of the electron.

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