Consider the hydrogen atom. The electric potential at a point P at a distance r from the nucleus can be modelled as 1 e V(P) = (1+2) ²* е 40 4mor (1) (a) What is the electric field created by the atom? (calculate at r > 0) (b) Consider a sphere of radius R around the nucleus. What is the charge inside this sphere? (Hint: Use Gauss' Law and the electric field you calculated in the previous part) (c) If you take the limit R→ 0, does the charge inside the sphere go to zero or takes a finite value?
Consider the hydrogen atom. The electric potential at a point P at a distance r from the nucleus can be modelled as 1 e V(P) = (1+2) ²* е 40 4mor (1) (a) What is the electric field created by the atom? (calculate at r > 0) (b) Consider a sphere of radius R around the nucleus. What is the charge inside this sphere? (Hint: Use Gauss' Law and the electric field you calculated in the previous part) (c) If you take the limit R→ 0, does the charge inside the sphere go to zero or takes a finite value?
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a and b
Transcribed Image Text:Consider the hydrogen atom. The electric potential at a point P at a
distance r from the nucleus can be modelled as
1 e
ATC F² ( 1 + 1 ) e - #
ao
V(P) =
(1)
(a) What is the electric field created by the atom? (calculate at r > 0)
(b) Consider a sphere of radius R around the nucleus. What is the
charge inside this sphere? (Hint: Use Gauss' Law and the electric
field you calculated in the previous part)
(c) If you take the limit R→ 0, does the charge inside the sphere go
to zero or takes a finite value?
(d) How can you interpret the finite value that you obtained in the
previous part?
(e) If you take the limit R→ ∞, does the charge inside the sphere go
to zero or takes a finite value? (is this atom neutral or not?)
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