A hydrogen atom has a single electron in circular orbit around a single proton.

Question

A hydrogen atom has a single electron in circular orbit around a single proton. The electron is bound to the proton through the electrostatic force between charged oppositely particles. The first three of the allowed orbits for the electron have radii of: r1 = 0.5x10-10 m; r2 = 2.0x10-10 m; r3 = 4.5x10-10 m

a. Determine the kinetic energy of an electron orbiting at each of these distances.

b. Determine the potential energy of an electron orbiting at each of these distances.

c. Find the energy needed to ionize the atom (have re --> infinity) for each of the orbits.

d. Determine the energy needed to move an electron from the r1 orbit to the r2 orbit.

Explanation / Answer

KE = Ze2/ 2r, PE = -Ze2/ r , here Z=1

KE1 = 2.56 * 10-28 V KE2=0.64 * 10-28 V KE3= 0.28 * 10-28 V

PE1=-5.12 * 10-28 V PE2=-1.28 * 10-28V PE3= -0.56 * 10-28V

Total Energy = -KE , at infinity KE = 0 hence energy required is same as KE at given orbit distance.

to move from orbit 1 to 2 dE = (2.56 - 0.64) * 10-28 = 1.92 * 10-28V

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