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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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Answer in one sentence:
Name the element that shows the simplest emission spectrum.
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For which one of the following, Bohr model is not valid?
In Bohr's model of hydrogen atom, the period of revolution of the electron in any orbit is proportional to ______.
In hydrogen atom, the de Broglie wavelength of an electron in the first Bohr's orbit is ____________.
[Given that Bohr radius, a0 = 52.9 pm]
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Which of the following models was successful in explaining the observed hydrogen spectrum?
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Angular speed of an electron in the ground state of hydrogen atom is 4 × 1016 rad/s. What is its angular speed in 4th orbit?
In Bohr model, speed of electron in nth orbit of hydrogen atom is ______. (b = Planck's constant, n = principal quantum number, ∈0 is the permittivity of free space, e = electronic charge)
In hydrogen atom, during the transition of electron from nth outer orbit to first Bohr orbit, a photon of wavelength `lambda` is emitted. The value of 'n' is [R =Rydberg's constant] ____________.
Using Bohr's quantization condition, what is the rotational energy in the second orbit for a diatomic molecule. (I = moment of inertia of diatomic molecule, h = Planck's constant)
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Show that the angular speed of an electron in the nth Bohr orbit is w = `(πme^4)/(2ε_0^2h^3n^3)` and the corresponding frequency of the revolution of the electron is f = `(me^4)/(4ε_0^2h^3n^3)`.
