NEET-XII-Physics
43: Bohr's Model and Physics of the Atom
- #3Which of the following products in a hydrogen atom are independent of the principal quantum number n? The symbols have their usual meanings.
(a) vn
(b) Er
(c) En
(d) vrdigAnsr: a,bAns : (a) vn
(b) Er
Relations for energy, radius of the orbit and its velocity are given by
`` E=-\frac{\,\mathrm{\,m\,}{Z}^{2}{\,\mathrm{\,e\,}}^{4}}{8{{\in }_{0}}^{2}{\,\mathrm{\,h\,}}^{2}{n}^{2}}``
`` r=\frac{{\in }_{0}{\,\mathrm{\,h\,}}^{2}{n}^{2}}{{\,\mathrm{\,\pi mZe\,}}^{2}}``
`` v=\frac{Z{\,\mathrm{\,e\,}}^{2}}{2{\in }_{0}\,\mathrm{\,h\,}n}``
Where
Z : the atomic number of hydrogen like atom
e : electric charge
h : plank constant
m : mass of electron
n : principal quantam number of the electron
`` {\in }_{0}`` : permittivity of vacuum
From these relations, we can see that the products independent of n are vn, Er.
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