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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.
According to Bohr's second postulate, the angular momentum of the electron is the integral multiple of `h/(2pi)`. The S.I unit of Plank constant h is the same as ______
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If aO is the Bohr radius and n is the principal quantum number then, state the relation for the radius of nth orbit of the electron in terms of Bohr radius and principal quantum number.
What is the energy of an electron in a hydrogen atom for n = ∞?
The angular momentum of an electron in the 3rd Bohr orbit of a Hydrogen atom is 3.165 × 10-34 kg m2/s. Calculate Plank’s constant h.
The magnifying power of a telescope is high, if its objective and eyepiece have respectively ____________.
When the electron in hydrogen atom jumps from fourth Bohr orbit to second Bohr orbit, one gets the ______.
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 ______.
If the speed of an electron of hydrogen atom in the ground state is 2.2 x 106 m/s, then its speed in the third excited state will be ______.
In hydrogen emission spectrum, for any series, the principal quantum number is n. Corresponding maximum wavelength λ is ______.
(R = Rydberg's constant)
The acceleration of electron in the first orbit of hydrogen atom is ______.
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The minimum energy required to excite a hydrogen atom from its ground state is ____________.
If a charge on the body is 1 nC, then how many electrons are present on the body?
When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes ____________.
Electron in Hydrogen atom first jumps from third excited state to second excited state and then from second excited state to first excited state. The ratio of the wavelengths λ1 : λ2 emitted in the two cases respectively is ______.
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 ______.
If Vn and Vp are orbital velocities in nth and pth orbit respectively, then the ratio Vp: Vn is ______.
An electron of mass m and charge e initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is ______.
When an electron in hydrogen atom revolves in stationary orbit, it ______.
Which of the following series of transition of hydrogen spectrum falls in visible region?
In Bohr’s atomic model, speed and time period of revolution of an electron in n = 3 level are respectively.
Calculate the radius of the first Bohr orbit in the hydrogen atom.
