EBK COLLEGE PHYSICS
EBK COLLEGE PHYSICS
11th Edition
ISBN: 8220103600385
Author: Vuille
Publisher: Cengage Learning US
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Chapter 28, Problem 50AP

(a)

To determine

The radii of the earth’s orbit of the hydrogen atom from Bohr model.

(a)

Expert Solution
Check Mark

Answer to Problem 50AP

The radii of the earth’s orbit of the hydrogen atom from Bohr model is rn=n22GMsME2 .

Explanation of Solution

Expression the angular momentum associated with the orbital motion of Earth to satisfy Bohr’s model is,

MEvr=nvn=nMErn (I)

  • vn is the nth level speed,
  • n is the nth energy level
  • ME is the Mass of earth
  • rn is the radius of the nth orbit

The gravitational force and the centripetal force compensate each other. So, the expression will be,

MEv2r=GMsMEr2v2=GMsr (II)

  • G is Gravitational constant,
  • Ms is the sun

Calculating the radius of the orbit by using the equation (I) and (II),

(nMErn)2=GMsrnrn=n22GMsME2

Conclusion:

Therefore, the radius of the earth’s orbit of the hydrogen atom from Bohr model is rn=n22GMsME2 .

(b)

To determine

The numerical value of n for the Sun-Earth system.

(b)

Expert Solution
Check Mark

Answer to Problem 50AP

The numerical value of n for the Sun-Earth system is 2.54×1074 .

Explanation of Solution

Formula to calculate the numerical value of n is,

rn=n22GMsME2

Substitute 5.98×1024kg for ME , 1.99×1030kg for Ms , 6.67×1011N-m2/kg2 for G , 1.496×1011m for r , 1.05×1034J-s for , to find the value of n ,

(1.496×1011m)=n2(1.05×1034J-s)2(6.67×1011N-m2)(1.99×1030kg)(5.98×1024kg)n=2.54×1074

Thus, the numerical value of n for the Sun-Earth system is 2.54×1074 .

Conclusion:

Therefore, the numerical value of n for the Sun-Earth system is 2.54×1074 .

(c)

To determine

The distance between the orbits for the quantum number n and the next orbit out from the sun corresponding to the quantum number (n+1) .

(c)

Expert Solution
Check Mark

Answer to Problem 50AP

The distance between the orbits for the quantum number n and the next orbit out from the sun corresponding to the quantum number (n+1) is 1.18×1063m .

Explanation of Solution

Formula to calculate the numerical value of n is,

(Δr)=rn+1rn=[(n+1)2n2]2GMsME2=(2n+1)2GMsME22n2GMsME2

Substitute 5.98×1024kg for ME , 1.99×1030kg for Ms , 2.54×1074 for n , 6.67×1011N-m2/kg2 for G , 1.05×1034J-s for , to find the value of n ,

(Δr)=2(2.54×1074)(1.05×1034J-s)2(6.67×1011N-m2/kg2)(1.99×1030kg)(5.98×1024kg)2=1.18×1063m

Thus, the distance between the orbits for the quantum number n and the next orbit out from the sun corresponding to the quantum number (n+1) is 1.18×1063m .

Conclusion:

Therefore, the distance between the orbits for the quantum number n and the next orbit out from the sun corresponding to the quantum number (n+1) is 1.18×1063m .

(d)

To determine

The significance of the computed result and the standard result for the distance.

(d)

Expert Solution
Check Mark

Answer to Problem 50AP

The computed result is much smaller than the standard result.

Explanation of Solution

The computed result is much smaller than the standard result. The standard value of the radius is in the range of 1015 . And the computed result is in the rage of ~1063 .

Thus, the computed result is much smaller than the standard result.

Conclusion:

Therefore, the computed result is much smaller than the standard result

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