Advertisements
Advertisements
प्रश्न
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the Coulomb attraction by a factor of about 10−40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
उत्तर
Radius of the first Bohr orbit is given by the relation,
`"r"_1 = (4pi in_0 ("h"/(2pi))^2)/("m"_"e" "e"^2)` .................(1)
Where,
∈0 = Permittivity of free space
h = Planck’s constant = 6.63 × 10−34 Js
me = Mass of an electron = 9.1 × 10−31 kg
e = Charge of an electron = 1.9 × 10−19 C
mp = Mass of a proton = 1.67 × 10−27 kg
r = Distance between the electron and the proton
Coulomb attraction between an electron and a proton is given as:
`"F"_"C" = "e"^2/(4piin_0 "r"^2)` .............(2)
Gravitational force of attraction between an electron and a proton is given as:
`"F"_"G" = ("Gm"_"p""m"_"e")/"r"^2` .........(3)
Where,
G = Gravitational constant = 6.67 × 10−11 N m2/kg2
If the electrostatic (Coulomb) force and the gravitational force between an electron and a proton are equal, then we can write:
∴ FG = FC
`("Gm"_"p""m"_"e")/"r"^2 = "e"^2/(4piin_0 "r"^2)`
∴ `"e"^2/(4piin_0) = "Gm"_"p""m"_"e"` ........(4)
Putting the value of equation (4) in equation (1), we get:
`"r"_1 = ("h"/(2pi))^2/("Gm"_"p""m"_"e"^2)`
= `(((6.63 xx 10^(-34))/(2xx3.14))^2)/(6.67 xx 10^(-11) xx 1.67 xx 10^(-27) xx (9.1 xx 10^(-31))^2) ~~ 1.21 xx 10^(29) "m"`
It is known that the universe is 156 billion light years wide or 1.5 × 1027 m wide. Hence, we can conclude that the radius of the first Bohr orbit is much greater than the estimated size of the whole universe.
APPEARS IN
संबंधित प्रश्न
Find the frequency of revolution of an electron in Bohr’s 2nd orbit; if the radius and speed of electron in that orbit is 2.14 × 10-10 m and 1.09 × 106 m/s respectively. [π= 3.142]
Using Bohr’s postulates, obtain the expression for total energy of the electron in the nth orbit of hydrogen atom.
Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?
A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10−6 m/s, then uncertainty in position is ≥ ____________.
(h = 6.6 × 10−34 J s)
According to Bohr's model of hydrogen atom, an electron can revolve round a proton indefinitely, if its path is ______.
Ratio of longest to shortest wavelength in Balmer series is ______.
Derive an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n – 1). Also show that for large values of n, this frequency equals to classical frequency of revolution of an electron.
According to the Bohr theory of H-atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:
In form of Rydberg's constant R, the wave no of this first Ballmer line is
The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
How will the energy of a hydrogen atom change if n increases from 1 to ∞?
The value of angular momentum for He+ ion in the first Bohr orbit is ______.
In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:
The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is ______.
A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ______.
(Given, Planck's constant = 6.6 × 10-34 Js)
State three postulates of Bohr's theory of hydrogen atom.
How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
