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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
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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