(a) Find the frequencies of revolution of electrons in n = 1 and n=2 Bohr orbits.
(b)What is the frequency of the photon emitted when an electron in an n=2 orbit drops to an n=1 hydrogen orbit?
(c )An electron typically spends about `10^(-8)s in an excited state before it drops to a lower state by emitteing a photon. How many revolutions does an electron in an n=2 Bohr hydrogen orbit make in `100xx10^(-8)` s?.

Answer

A, B, C, D

Explanation

(a) f=(v)/(2pix)
`f_1 = ((2.2xx10^6)/(2pi)(0.529xx10^(-10)`
`~~6.6xx10^(15) Hz`
`vprop(1)/(n) and r prop n^2`
`fprop (v)/(r ) rArr f prop (1)/(n^3)`
`:. F_2 = (f_1)/(8).` (b) `DeltaE =E_2 -E_1=10.2 eV = hf`
`:.f = (10.2xx1.6xx10^(-19)/(6.6xx10^(-34)`
`~~2.46xx10^(15) Hz`
(c) in option (a), we have found that
`f_2 = 0.823xx10^(15) Hz`
`T_2 = (1)/(f_2)`
`N = (t)/(T_2) = tf_2 = (10^(-8)(0.823xx10^(15)`
`=8.23xx10^6 revolutions`.