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Which of the Following Curves May Represent the Speed of the Electron in a Hydrogen Atom as a Function of the Principal Quantum Number N?

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प्रश्न

Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of trincipal quantum number n?

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उत्तर

(c)

The speed (v) of electron can be expressed as

   `v = (Ze^2)/(2∈_0hn)` ....(1)

Here,

Z = Number of protons in the nucleus

e = Magnitude of charge on electron charge

n = Principal quantum number

h = Planck's constant

It can be observed from equation (1) that the velocity of electron is inversely proportional to the principal quantum number (n).
Therefore, the graph between them must be a rectangular hyperbola.
The correct curve is (c).

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अध्याय 43: Bohr’s Model and Physics of Atom - MCQ [पृष्ठ ३८३]

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एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 43 Bohr’s Model and Physics of Atom
MCQ | Q 7 | पृष्ठ ३८३

संबंधित प्रश्न

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, a thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10−10 m).

(a) Construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.

(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.


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