Neutral hydrogen can be modeled as a positive point charge + 1.6 × 10 −19 C surrounded by a distribution of negative charge with volume density given by ρ E ( r ) = − A e − 2 r / a 0 where a 0 = 0.53 × 10 −10 m is called the Bohr radius, A is a constant such that the total amount of negative charge is −1.6 × 10 −9 C, and e = 2.718 ⋯ is the base of the natural log. ( a ) What is the net charge inside a sphere of radius a 0 ? ( b ) What is the strength of the electric field at a distance a 0 from the nucleus? [ Hint : Do not confuse the exponential number e with the elementary charge e which uses the same symbol but has a completely different meaning and value ( e = 1.6 × 10 −19 C).]
Neutral hydrogen can be modeled as a positive point charge + 1.6 × 10 −19 C surrounded by a distribution of negative charge with volume density given by ρ E ( r ) = − A e − 2 r / a 0 where a 0 = 0.53 × 10 −10 m is called the Bohr radius, A is a constant such that the total amount of negative charge is −1.6 × 10 −9 C, and e = 2.718 ⋯ is the base of the natural log. ( a ) What is the net charge inside a sphere of radius a 0 ? ( b ) What is the strength of the electric field at a distance a 0 from the nucleus? [ Hint : Do not confuse the exponential number e with the elementary charge e which uses the same symbol but has a completely different meaning and value ( e = 1.6 × 10 −19 C).]
Neutral hydrogen can be modeled as a positive point charge + 1.6 × 10−19 C surrounded by a distribution of negative charge with volume density given by
ρ
E
(
r
)
=
−
A
e
−
2
r
/
a
0
where a0 = 0.53 × 10−10 m is called the Bohr radius, A is a constant such that the total amount of negative charge is −1.6 × 10−9 C, and
e
=
2.718
⋯
is the base of the natural log. (a) What is the net charge inside a sphere of radius a0? (b) What is the strength of the electric field at a distance a0 from the nucleus? [Hint: Do not confuse the exponential number e with the elementary charge e which uses the same symbol but has a completely different meaning and value (e = 1.6 × 10−19C).]
Solar wind is a flow of heavily charged ions emanating from the Sun’s corona. Spectroscopic analysis suggests it contains a density of approximately 5.0 electrons per cubic centimeter (cm3). Given that the elementary charge ? ≈ 1.6 × 10−19 ? and using the combined average of your measured values of Q 0.0375nC, determine the charge density of a cubic meter (m3) of solar wind sample as a function of Q
Solar wind is a flow of heavily charged ions emanating from the Sun’s corona. Spectroscopic analysis suggests it contains a density of approximately 5.0 electrons per cubic centimeter (cm3). Given that the elementary charge and using the combined average of your measured values of Q, determine the charge density of a cubic meter (m3) of solar wind sample as a function of Q.
Qav = -6.1095 * 10-9 C
A hydrogen atom can be considered as having a central pointlike proton of positive charge e and an electron of negative charge -e that is distributed about the proton according to the volume charge density r = A exp(-2r/a0). Here A is a constant, a0 = 0.53 *10-10 m, and r is the distance from the center of the atom. (a) Using the fact that the hydrogen is electrically neutral, find A. Then find the (b) magnitude and (c) direction of the atom’s electric field at a0.
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