College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 28, Problem 11P

(a)

To determine

The radius of the orbit.

(a)

Expert Solution
Check Mark

Answer to Problem 11P

The radius of the orbit 0.212nm .

Explanation of Solution

Given Info: The Bohr radius is 0.0529nm .

Formula to calculate the radius is,

r=n2ao

  • r is radius of the orbit
  • n is energy level
  • ao is the Bohr radius

Substitute 2 for n , 0.0529nm for ao to find r .

r=(2)2(0.0529nm)=0.212nm

Thus, the radius of the orbit is 0.212nm

Conclusion:

Therefore, the radius of the orbit is 0.212nm .

(b)

To determine

The linear momentum of the electron.

(b)

Expert Solution
Check Mark

Answer to Problem 11P

The linear momentum of the electron is 9.95×1025kg-m/s .

Explanation of Solution

From unit conversion,

1nm=1×109m

Formula to calculate the momentum is,

p=mke2r

  • r is radius of the orbit
  • m is mass of electron
  • e is the charge of electron
  • k is Coulomb’s constant
  • p is momentum of the electron

Substitute 1.6×1019C for e , 0.212nm for r , 9.1×1031kg for m , 9×109N-m2/C2 for k to find p .

p=(9.1×1031kg)(9×109N-m2/C2)(1.6×1019C)2(0.212nm)(1×109nm1m)=9.95×1025kg-m/s

Thus, the momentum of the electron is 9.95×1025kg-m/s .

Conclusion:

Therefore, the momentum of the electron is 9.95×1025kg-m/s .

(c)

To determine

The angular momentum of the electron.

(c)

Expert Solution
Check Mark

Answer to Problem 11P

The angular momentum of the electron is 2.11×1034J-s .

Explanation of Solution

Formula to calculate the angular momentum is,

L=n(h2π)

  • L is angular momentum of the electron
  • n is state
  • h is the Planck’s constant

Substitute 2 for n , 6.63×1034J-s for h , to find L .

L=(2)(6.63×1034J-s2π)=2.11×1034J-s

Thus, the angular momentum of the electron is 2.11×1034J-s .

Conclusion:

Therefore, the angular momentum of the electron is 2.11×1034J-s .

(d)

To determine

The kinetic energy of the electron.

(d)

Expert Solution
Check Mark

Answer to Problem 11P

The kinetic energy of the electron is 3.4eV .

Explanation of Solution

Formula to calculate the kinetic energy is,

K.E=p22m

  • p is linear momentum of the electron
  • m is mass of the electron

From unit conversion,

1eV=1.6×1019J

Substitute 9.95×1025kg-m/s for p , 9.1×1031kg for m , to find K.E .

K.E=(9.95×1025kg-m/s)22(9.1×1031kg)(1eV1.6×1019J)=3.4eV

Thus, the kinetic energy of the electron is 3.4eV .

Conclusion:

Therefore, the kinetic energy of the electron is 3.4eV .

(e)

To determine

The potential energy of the electron.

(e)

Expert Solution
Check Mark

Answer to Problem 11P

The potential energy of the electron is 6.8eV .

Explanation of Solution

Formula to calculate the potential energy is,

P.E=ke2r

  • k is coulomb’s constant
  • e is the electronic charge
  • r is radius of the orbit

From unit conversion,

1eV=1.6×1019J

1nm=1×109m

Substitute 9×109N-m2/C2 for k , 1.6×1019C for e , 0.212nm for r , to find P.E .

P.E=(9×109N-m2/C2)(1.6×1019C)2(0.212nm)(1×109m1nm)(1eV1×1019J)=6.8eV

Thus, the potential energy of the electron is 6.8eV .

Conclusion:

Therefore, the potential energy of the electron is 6.8eV .

(f)

To determine

The total energy of the electron.

(f)

Expert Solution
Check Mark

Answer to Problem 11P

The total energy of the electron is 3.4eV .

Explanation of Solution

Formula to calculate the total energy is,

E=K.E+P.E

  • E is total energy
  • K.E is the kinetic energy electron
  • P.E is potential energy of the electron.

Substitute 3.4eV for K.E , 6.8eV for P.E , to find E .

E=(3.4eV)+(6.8eV)=3.4eV

Thus, the total energy of the electron is 3.4eV .

Conclusion:

Therefore, the total energy of the electron is 3.4eV

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