Check that the ratio ke2/G memp is dimensionless. Look up a Tableof Physical Constants and determine the value of this ratio. Whatdoes the ratio signify?
The given ratio is k e 2 G m e m p .
The unit of gravitational constant G is N ⋅ m 2 / kg 2 .
The term k is a constant which has unit of N ⋅ m 2 / C 2 .
The unit of charge e is C .
The unit of mass of electron and proton m e and m p is kg .
The unit of the given ratio is,
k e 2 G m e m p = [ N ⋅ m 2 / C 2 ] × [ C ] 2 [ N ⋅ m 2 / kg 2 ] [ kg ] [ kg ] = 1
Thus, the given ratio is unit less.
The value of e is 1.6 × 10 − 19 C .
The value of G is 6.67 × 10 − 11 N ⋅ m 2 / kg 2 .
The value of k is 9 × 10 9 N ⋅ m 2 / C 2 .
The values of m e and m p are 9.1 × 10 − 31 kg and 1.66 × 10 − 27 kg respectively.
The given ratio is,
k e 2 G m e m p
Substituting the values in the above expression, we get:
k e 2 G m e m p = 9 × 10 9 N ⋅ m 2 / C 2 × ( 1.6 × 10 − 19 C ) 2 6.67 × 10 − 11 N ⋅ m 2 / kg 2 × 9.1 × 10 − 31 kg × 1.66 × 10 − 27 kg ≈ 2.4 × 10 39
The given ratio is the ratio of electrostatic force to gravitational force acting between an electron and a proton.
The given ratio is
The unit of gravitational constant
The term
The unit of charge
The unit of mass of electron and proton
The unit of the given ratio is,
Thus, the given ratio is unit less.
The value of
The value of
The value of
The values of
The given ratio is,
Substituting the values in the above expression, we get:
The given ratio is the ratio of electrostatic force to gravitational force acting between an electron and a proton.
