Hydrogen is a flammable, nontoxic, colorless, odorless, and tasteless gas. The U
ID: 1702115 • Letter: H
Question
Hydrogen is a flammable, nontoxic, colorless, odorless, and tasteless gas. The U.S. produces 100 billion cubic feet per year of hydrogen for industry and for the space program. A hydrogen atom consists of an electron (9.11×10–31 kg) and a proton (1.67×10–27 kg). (a) What is the net charge of a hydrogen atom? (b) Find the ratio of the electric to the gravitational force between the electron and the proton (e 1.60×10–19 C). (c) Suppose we adjusted the mass of the proton so that the ratio is 1. What would be the new mass of the proton? (d) Instead, suppose we adjusted the elementary charge, e, so that the ratio is 1. What would be the new elementary charge?(a) ______ C
(b) ________
(c) ________ kg
(d) __________ C
Explanation / Answer
a) net charge of hydrogen atom is zero because numbar of electrons is equal to number of protons
b)the electric force between electron and proton is
F_ E = k q1 q2 / r^2
gravitational force bet ween electron and proton is
F _G = G m1 m2 / r^2
ratio of the electric to the gravitational force between the electron and the proton is
F _E / F _G = k q1 q2 / G m1 m2
where q1 and q1 are the charge of electron and proton
m1 and m2 are masses of electron and proton
= (9*10^ 9 ) (1.6*10^ -19) ^2 / ( 6.693*10^ -11)(1.6*10^ -27 )(9.1*10^ -31 )
= 0.23 10^ 40
c) Suppose we adjusted the mass of the proton so that the ratio is 1
k q1 q2 / G m1 m2 =1
(9*10^ 9 ) (1.6*10^ -19) ^2 / ( 6.693*10^ -11)(m_p )(9.1*10^ -31 )=1
0.378*10^ 13 / m_ p = 1
so mass of proton = 3.78*10^ 12 kg
d) suppose we adjusted the elementary charge, e, so that the ratio is 1
k q1 q2 / G m1 m2 =1
(9*10^ 9 ) (q) ^2 / ( 6.693*10^ -11)(1.6*10^ -27 )(9.1*10^ -31 )=1
q = 3.29*10^ -39 C
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