Velocity of Electron ionized from Hydrogen

AI Thread Summary
Ultraviolet light with a wavelength of 45.0 nm ionizes hydrogen atoms, releasing electrons with a kinetic energy of 14 eV. The calculated velocity of these electrons was found to be 5.54 x 10^15 m/s, which exceeds the speed of light, indicating a miscalculation. The correct approach involves converting kinetic energy from electronvolts to joules before calculating velocity. Emphasizing the importance of unit consistency, the discussion highlights the need for careful unit management in physics calculations. Properly addressing these aspects ensures accurate results in quantum mechanics problems.
DRC12
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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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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
 
Oh, thanks, I keep forgetting about that. I really need to start writing down the units
 
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
 
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