A hydrogen atom is made up of a proton of charge +Q = -1.60 x 10-19 C and an electron of charge -Q = -1.60 x 10-19 C. The proton may be regarded as a point EXECUTE charge at r = 0, the center of the atom. The motion of the electron causes its charge to be "smeared out" into a spherical distribution around the proton (Eigure 1), so that the electron is equivalent to a charge per unit volume of p(r) = -(Q/Tan)e 2r/ag where ag = 5.29 x 10-11 m is called the Bohr radius. (a) Find the total Part C Integrate the expression and solve the linear system from previous part to find the total charge Q(r)encl within radius r. amount of the hydrogen atom's charge that is enclosed within a sphere with radius r centered on the proton. (b) Find the electric field (magnitude and direction) caused by the charge of the hydrogen atom as a function of r. c) Make a graph as a function of r of the ratio of the electric-field magnitude E to the magnitude of Express your answer in terms of the variables Q, r, and ao. the field due to the proton alone. ? Figure 1 of 1 Q(r)encd = Proton: point charge +C Electron: charge -0 "smeared out" in a spherical distribution

icon
Related questions
Question
A hydrogen atom is made up of a proton of charge
+Q = -1.60 x 10-19 C and an electron of charge
-Q = -1.60 x 10-19 C. The proton may be regarded as a point
charge at r = 0, the center of the atom. The motion of the electron
causes its charge to be "smeared out" into a spherical distribution
around the proton (Figure 1), so that the electron is equivalent to a
charge per unit volume of p(r) = -(Q/Tao)e 2r/a0, where
ao = 5.29 x 10-11 m is called the Bohr radius. (a) Find the total
EXECUTE
Part C
Integrate the expression and solve the linear system from previous part to find the total charge Q(r)encl within radius r.
amount of the hydrogen atom's charge that is enclosed within a
sphere with radius r centered on the proton. (b) Find the electric
field (magnitude and direction) caused by the charge of the
hydrogen atom as a function of r.c) Make a graph as a function of
r of the ratio of the electric-field magnitude E to the magnitude of
the field due to the proton alone.
Express your answer in terms of the variables Q, r, and ao.
?
Figure
< 1 of 1
Q(r)encl =
Proton:
point charge +Q
Electron:
charge -0 "smeared out"
in a spherical distribution
Transcribed Image Text:A hydrogen atom is made up of a proton of charge +Q = -1.60 x 10-19 C and an electron of charge -Q = -1.60 x 10-19 C. The proton may be regarded as a point charge at r = 0, the center of the atom. The motion of the electron causes its charge to be "smeared out" into a spherical distribution around the proton (Figure 1), so that the electron is equivalent to a charge per unit volume of p(r) = -(Q/Tao)e 2r/a0, where ao = 5.29 x 10-11 m is called the Bohr radius. (a) Find the total EXECUTE Part C Integrate the expression and solve the linear system from previous part to find the total charge Q(r)encl within radius r. amount of the hydrogen atom's charge that is enclosed within a sphere with radius r centered on the proton. (b) Find the electric field (magnitude and direction) caused by the charge of the hydrogen atom as a function of r.c) Make a graph as a function of r of the ratio of the electric-field magnitude E to the magnitude of the field due to the proton alone. Express your answer in terms of the variables Q, r, and ao. ? Figure < 1 of 1 Q(r)encl = Proton: point charge +Q Electron: charge -0 "smeared out" in a spherical distribution
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 4 images

Blurred answer
Similar questions