Principal Quantum number by size?

AI Thread Summary
The discussion centers on calculating the principal quantum number (n) for a hydrogen atom to achieve a size of one micron, using the formula r=(5.3x10^-11)(n^2). The calculation yields n approximately equal to 97, raising questions about the practicality of such a high quantum number since typical values range from 1 to 6. It is noted that while n can theoretically extend to infinity, in practice, an atom with such a high n would likely lose its electron due to collisions. The conversation concludes with an acknowledgment of the complexities involved in such high quantum states. Understanding these quantum numbers is crucial for grasping atomic behavior at extreme scales.
physics(L)10
Messages
101
Reaction score
0

Homework Statement


What is the value of the principal quantum number for a hydrogen atom to have a size of one micron?

Homework Equations


r=(5.3x10-11)(n2)
r=1x10-6/2=5x10-7

The Attempt at a Solution



5x10-7=(5.3x10-11)(n2)

97.1 = n

How is this possible? lol Maybe it's more complicated then I'm thinking.
 
Physics news on Phys.org
Just use the nearest integer value.
 
So I'm right? The answer is just 97? I thought the principal quantum numbers (n) only go up to like 5 or 6 or something like that though.
 
Yes, you're right. n can go up to infinity in theory. In practice, an atom with such a high n would eventually collide with another atom or perhaps a container wall, and completely lose the electron.
 
Alrighty, thank you very much :)
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top