A hydrogen atom is in its third excited state ( n = 4). Using the Bohr theory of

Question

A hydrogen atom is in its third excited state (n = 4). Using the Bohr theory of the atom, calculatethe following. (a) the radius of the orbit
1 nm
(b) the linear momentum of the electron
2 kg·m/s
(c) the angular momentum of the electron
3 J·s
(d) the kinetic energy
4 eV
(e) the potential energy
5 eV
(f) the total energy
6 eV A hydrogen atom is in its third excited state (n = 4). Using the Bohr theory of the atom, calculatethe following. (a) the radius of the orbit
1 nm
(b) the linear momentum of the electron
2 kg·m/s
(c) the angular momentum of the electron
3 J·s
(d) the kinetic energy
4 eV
(e) the potential energy
5 eV
(f) the total energy
6 eV (a) the radius of the orbit
1 nm
(b) the linear momentum of the electron
2 kg·m/s
(c) the angular momentum of the electron
3 J·s
(d) the kinetic energy
4 eV
(e) the potential energy
5 eV
(f) the total energy
6 eV

Explanation / Answer

(a)    rn = n2 ao    where ao = 0.0529 nm    rn = ............ nm (b)    me is mass of the electron    in our problem n = 3    as the electric force is supplying the necessarycentripetal force we can write    me vn2 /rn = ke e2 /rn2 which gives    vn = kee2 / me rn    we knoe that momentum = mass x velocity, so wecan get momentum as    pn = mevn         =me ke e2 /rn         = ...........kg.m/s (c)    the angular momentum of the electronwill be    Ln = n h / 2         =..................... J.s (d)    kinetic energy KEn = (1 / 2)me vn2                               = ..................... m / s (e)    PEn = (ke)(-e)(e) /rn           =................ J (f)    the total energy will be    En = KEn +PEn         =...................J                       =...................J              

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