Advertisements
Advertisements
प्रश्न
State Bohr’s third postulate for hydrogen (H2) atom. Derive Bohr’s formula for the wave number. Obtain expressions for longest and shortest wavelength of spectral lines in ultraviolet region for hydrogen atom
Advertisements
उत्तर
Third postulate (Transition and frequency condition):-
As long as electron remains in one of the stationary orbits, it does not radiate energy. Whenever an electron jumps from higher stationary orbit to lower stationary orbit, it radiates energy equal to the difference in energies of the electron in the two orbits.
Bohr’s formula for spectral lines in hydrogen spectrum:-
i. Let, En = Energy of electron in nth higher orbit
Ep = Energy of electron in pth lower orbit
ii. According to Bohr’s third postulate,
En - Ep = hv
∴ v = (Ea - Ep)/h ...........(1)
iii. `"But "E_n=-(me^4)/(8epsilon_0^2"h"^2"n"^2)` ............(2)
`E_p=-(me^4)/(8epsilon_0^2"h"^2"p"^2` .............(3)
iv. From equations (1), (2) and (3),
`"v"=(((-me^4)/(8epsilon_0^2"h"^2"n"^2))-(-(me^4)/(8epsilon_0^2"h"^2"p"^2)))/h`
`therefore"v"=(me^4)/(8epsilon_0^2h^3)[-1/n^2+1/p^2]`
`thereforec/lambda=(me^4)/(8epsilon_0^2h^3)[1/p^2-1/n^2]` [∵ v = c/λ]
where, c = speed of electromagnetic radiation
`therefore1/lambda=(me^4)/(8epsilon_0^2h^3c)[1/p^2-1/n^2]`
v. `1/lambda=R[1/p^2-1/n^2]` ............(4)
`"where, "(me^4)/(8epsilon_0^2h^3c)=R="Rydberg’s constant"`
Equation (4) represents Bohr’s formula for hydrogen spectrum.
vi. 1/λ is called wave number (`bar"v"` ) of the line.
`thereforebar"v"=1/lambda=R(1/p^2-1/n^2)`
For longest wavelength in ultraviolet region (Lyman series),
p = 1; n = 2
`therefore1/lambda_(L_1)=R(1/1^2-1/2^2)=(3R)/4`
`thereforelambda_(L_1)=4/(3R)`
For shortest wavelength in ultraviolet region
P = 1; n = ∞
`therefore1/lambda_(L_2)=R(1/1^2-1/oo^2)=R`
`thereforelambda_(L_2)=1/R`
APPEARS IN
संबंधित प्रश्न
An electron is orbiting in 5th Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.
If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1, calculate the energy with which it is bound to the nucleus.
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.
Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Nelgect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10−24 kg. Mass of the sun = 2.0 × 1030 kg, earth-sun distance = 1.5 × 1011 m.
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?
Obtain Bohr’s quantisation condition for angular momentum of electron orbiting in nth orbit in hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.
How are various lines of Lyman series formed? Explain on the basis of Bohr’s theory.
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
Calculate the de-Broglie wavelength associated with the electron revolving in the first excited state of the hydrogen atom. The ground state energy of the hydrogen atom is −13.6 eV.
According to Bohr's theory, an electron can move only in those orbits for which its angular momentum is integral multiple of ____________.
The spectral line obtained when an electron jumps from n = 5 to n = 2 level in hydrogen atom belongs to the ____________ series.
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)
The radius of the third Bohr orbit for hydrogen atom is ____________.
According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.
Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?
When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy?
Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.
If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å, and (ii) R = 10 Å.
According to Bohr atom model, in which of the following transitions will the frequency be maximum?
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 ______.
The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the nth to second Bohr orbit. The value of n is ______.
In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is ______.
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
What is the velocity of an electron in the 3rd orbit of hydrogen atom if its velocity in the 1st orbit is v0?
Calculate the energy associated with third orbit of He+.
Energy and radius of first Bohr orbit of He+ and Li2+ are:
[Given RH = −2.18 × 10−18 J, a0 = 52.9 pm]
