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Atoms — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAtoms5 Marks
Question
Write Bohr's postulates of hydrogen atom.
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Answer

Bohr's Postulates : (i) An atom consists of a very tiny positively charged nucleus. Nearly the entire mass of the atom is concentrated in the nucleus.
(ii) The electrons in an atom revolve around the nucleus in certain permitted circular orbits. The electrostatic force of attraction between the electron and the nucleus provides the necessary centripetal force.
(iii) An electron can revolve only in those orbits for which its orbital angular momentum is an integral multiple of $\frac{h}{2 \pi}$. Here, h is a universal constant known as Planck's constant $=6.63 \times 10^{-34} Js$
If $r$ is the radius of a permitted orbit, $m$ is the mass of the electron and $v$ is the velocity of the electron in that orbit, then
$m v r=n\left(\frac{h}{2 \pi}\right)$
where $n$ is an integer known as principle quantum number and has integral values 1, 2, 3, ...This relation is regarded as a quantisation condition for the angu-lar momentum of the electron
(iv) An electron revolving in a permitted orbit does not radiate energy though it is accelerating. So, the total energy of the electron remains constant. The permitted orbits are called stationary or non-radiating orbits. By introducing the concept of stationery orbit, Bohr could explain the stability of the atomic structure.
(v) When an electron jumps from higher orbit to lower orbit, electromagnetic radiation is emitted.
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On the other hand, there is absorption of energy when an electron jumps from lower orbit to higher orbit. Consider two orbits of principle quantum numbers n1 and n2 Let En1 and En2 be the energies associated with respective orbits. The frequency of the emitted radiation is given by
$h \nu= E _{n_2}- E _{n_1}$
$\Rightarrow \quad v=\left(\frac{E_{n_2}-E_{n_1}}{h}\right)$
It is obvious that emission of energy from a atom takes place only when an electron jumps from higher energy level to any lower level. Hence in the energy emitted by an atom has only some definite frequency waves. If the spectrum of this energy it taken it is obtained as a line spectrum, in which there are many sharp lines.

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