Using the Bohr model for hydrogen, please answer the following: (a) Calculate th

Question

Using the Bohr model for hydrogen, please answer the following:

(a) Calculate the time required for an electron in the n = 2 state to complete one orbit around the nucleus.

__________________ s

(b) The typical "lifetime" of an electron in the first excited state (n = 2) is roughly 10-8 s -- after this time the electron is likely to have returned to the ground state (n = 1). Estimate the number of orbits an electron completes in the first excited state before dropping back down to the ground state.

______________ orbits

Explanation / Answer

a) r = a0 n^2 / z

r = 0.0529 x 2^2 nm = 0.2116 nm

KE = - E = 13.6/n^2 eV = 3.4 eV

(9.109 x 10^-31 x v^2 /2 ) = 3.4 x 1.6 x 10^-19

v = 1.09 x 10^6

T = 2pi r /v = (2 x pi x 0.2116 x 10^-9 ) / (1.09 x 10^6)

     = 1.2165 x 10^-15 sec

b) number of rounds = 10^-8 / (1.2165 x 10^-15)

      = 8.22 x 10^6 orbits

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