Advertisements
Advertisements
рдкреНрд░рд╢реНрди
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.
рдЙрддреНрддрд░
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"`
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
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 ______
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.
Calculate the longest wavelength in the Paschen series.
(Given RH =1.097 ×107 m-1)
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 ____________.
How many moles of electrons are required for reduction of 9 moles of Cr3+ to Cr?
If the ionisation potential of helium atom is 24.6 volt, the energy required to ionise it will be ____________.
The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively ______.
In Bohr's model of hydrogen atom, the period of revolution of the electron in any orbit is proportional to ______.
When hydrogen atom is in its first excited level, its radius is how many time its ground state radius?
In hydrogen emission spectrum, for any series, the principal quantum number is n. Corresponding maximum wavelength λ is ______.
(R = Rydberg's constant)
When an electron in hydrogen atom is excited from its 3rd to 5th stationary orbit, tbe change in angular momentum of electron is (Planck's constant: h = 6.62 x 10-34 Js) ____________.
In hydrogen spectnun, the wavelengths of light emited in a series of spectral lines is given by the equation `1/lambda = "R"(1/3^2 - 1/"n"^2)`, where n = 4, 5, 6 .... And 'R' is Rydberg's constant.
Identify the series and wavelenth region.
If a charge on the body is 1 nC, then how many electrons are present on the body?
If n is principal quantum number and r is the radius of the orbit in which electron revolves around nucleus, then its kinetic energy is ____________.
When an electron in hydrogen atom jumps from third excited state to the ground state, the de-Broglie wavelength associated with the electron becomes ____________.
The de-Broglie wavelength of an electron in 4th orbit is ______.
(r = radius of 1st orbit)
When an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength 'λ'. When it jumps from the fourth orbit to third orbit, the wavelength emitted by the photon will be ______.
If Vn and Vp are orbital velocities in nth and pth orbit respectively, then the ratio Vp: Vn is ______.
The relation between magnetic moment of revolving electron 'M' and principle quantum number 'n' is ______.
The ground state energy of the hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the second excited state is respectively ______
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 ______.
The orbital frequency of an electron in the hydrogen atom ______.
The speed of an electron in ground state energy level is 2.6 × 106 ms-1, then its speed in third excited state will be ______.
Ultraviolet light of wavelength 300 nm and intensity 1.0 Wm−2 falls on the surface of a photosensitive material. If one percent of the incident photons produce photoelectrons, then the number of photoelectrons emitted from an area of 1.0 cm2 of the surface is nearly ______.
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.
What is the origin of spectral lines? Obtain an expression for the wave number of a line in hydrogen spectrum.
Compute the shortest and the longest wavelength in the Lyman series of hydrogen atom.
