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Question
Which 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) vr
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Solution
(a) vn
(b) Er
Relations for energy, radius of the orbit and its velocity are given by
`E=-(mZ^2e^4)/(8∈_0^2h^2n^2 )`
`r = (∈_0h^2n^2)/(pimZe^2)`
`v = (Ze^2)/(2∈_0hn)`
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
∈_0 : permittivity of vacuum
From these relations, we can see that the products independent of n are vn, Er.
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