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# Some Typical Kinetic Energies. (a) In the Bohr model of

ISBN: 9780321675460 31

## Solution for problem 16E Chapter 6

University Physics | 13th Edition

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Problem 16E

Some Typical Kinetic Energies.? (a) In the Bohr model of the atom, the ground-state electron in hydrogen has an orbital speed of 2190 km/s. What is its kinetic energy? (Consult Appendix F.) (b) If you drop a 1.0-kg weight (about 2 lb) from a height of 1.0 m, how many joules of kinetic energy will it have when it reaches the ground? (c) Is it reasonable that a 30-kg child could run fast enough to have 100 J of kinetic energy?

Step-by-Step Solution:

Solution 16E Step 1 of 5: (a) In the Bohr model of the atom, the ground-state electron in hydrogen has an orbital speed of 2190 km/s. What is its kinetic energy (Consult Appendix F.) In the given problem, we need to calculate kinetic energy of electron in ground state moving with speed v=2190 km/s and mass m = 9.1e9 × 10 31kg To convert speed from km/s to m/s 3 3 Using 1km =10 m v=2190× 10 m/s The kinetic energy of the electron is given by, 1 2 KE= 2 m e Substituting v=2190× 10 m/s and m = 9.e09 × 10 31kg 1 31 3 2 KE= 2 (9.109 × 10 kg)(2190 × 10 m/s) 19 KE = 21.84× 10 J Step 2 of 5: To convert Energy in joules to electron volt 19 21.84×101J Using 1eV=1.6× 10 J KE= 1.6×101J KE=13.65 eV Therefore, the kinetic energy of the electron is 21.84× 10 19J or 13.65 eV. Step 3 of 5: (b) If you drop a 1.0-kg weight (about 2 lb) from a height of 1.0 m, how many joules of kinetic energy will it have when it reaches the ground From law of conservation of energy, when the object falls from certain height; the change in Kinetic energy will be equal to change in gravitational potential energy. As shown below,

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