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Starting with ЁЭСЯ = `(ε_0h^2n^2)/(pimZe^2),` Show that the speed of an electron in nth orbit varies inversely to principal quantum number.
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According to Bohr’s second postulate,
mrnvn = `"nh"/(2pi)`
∴ `"m"^2"v"_"n"^2"r"_"n"^2 = ("n"^2"h"^2)/(4pi^2)`
∴ `"v"_"n"^2 = ("n"^2"h"^2)/(4pi^2"m"^2"r"_"n"^2)`
Substituting, rn = `(ε_0"h"^2"n"^2)/(pi"m""Z""e"^2)` in above relation,
`"v"_"n"^2 = ("n"^2"h"^2)/(4pi^2"m"^2) xx ((pi"m"Z""e""^2)/(epsilon_0"h"^2"n"^2))^2`
= `("n"^2"h"^2)/(4pi^2"m"^2) xx (pi^2"m"^2"Z"^2"e"^4)/(epsilon_0^2"h"^4"n"^4)`
= `("Z"^2"e"^4)/(4epsilon_0^2"h"^2"n"^2)`
∴ `"v"_"n"^2 ∝ 1/"n"^2`
⇒ `"v"_"n" ∝ 1/"n"`
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Linear momentum of an electron in Bohr orbit of H-atom (principal quantum number n) is proportional to ______.
Answer in brief.
State the postulates of Bohr’s atomic model.
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Calculate the wavelength for the first three lines in the Paschen series.
(Given RH =1.097 ×107 m-1)
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[Given that Bohr radius, a0 = 52.9 pm]
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The minimum energy required to excite a hydrogen atom from its ground state is ____________.
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(b =Planck's constant)
The radius of orbit of an electron in hydrogen atom in its ground state is 5.3 x 10-11 m After collision with an electron, it is found to have a radius of 13.25 x 10-10 m. The principal quantum number n of the final state of the atom is ______.
The relation between magnetic moment of revolving electron 'M' and principle quantum number 'n' is ______.
When an electron in hydrogen atom revolves in stationary orbit, it ______.
Let Ee and Ep represent the kinetic energy of electron and photon, respectively. If the de-Broglie wavelength λp of a photon is twice the de-Broglie wavelength λe of an electron, then `E_p/E_e` is ______.
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In Bohr’s atomic model, speed and time period of revolution of an electron in n = 3 level are respectively.
Find the momentum of the electron having de Broglie wavelength of 0.5 A.
Compute the shortest and the longest wavelength in the Lyman series of hydrogen atom.
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