I am trying to solve the above problem. However, I am supposed to solve it with the following values:
Particle is an electron, so:
Essentially I am supposed to find the conditions for which no solution is possible using a graphical method. This is where I am stuck. The book that I have does not discuss the graphical method, so I am not sure where to begin with it or where the values come in to play. I have solved it using a traditional method seen below:
The Attempt at a Solution
As can be seen above:
since kLcsc(kL)=kL/sin(kL) can never be smaller than one, (2mUL^2)/h^2 < 1
Also, since sin(kL) is in the denominator, no solutions would be possible when kL is equal to zero or a multiple of π.
To do it graphically, would I simply draw a graph of kLcsc(kL) and show where it is undefined? I am confused. Also where would the values I was given come into play?
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