Advertisements
Advertisements
प्रश्न
Obtain an expression for the radius of Bohr orbit for H-atom.
उत्तर
Let us consider an electron revolving around the nucleus in a circular orbit of radius ‘r’.
According to Bohr’s first postulate, the centripetal force is equal to the electrostatic force of attraction. That is
`"mv"^2/"r"=1/(4piepsilon_o)xx"e"^2/"r"^2`
`"Or,""v"^2="e"^2/(4piepsilon_o"mr")` -------------------(1)
According to the Bohr's second postulate:
`"Angular momentum"= "n""h"/(2pi)`
`"mvr"="n""h"/(2pi)`
Or, `"v"="nh"/(2pi"mr")` -----------------(2)
Or, `"v"^2=("n"^2"h"^2)/(4pi^2"m"^2"r"^2)` ---------------------(3)
Comparing eqn (1) and eqn (3), we get
`"e"^2/(4piepsilon_o"mr")=("n"^2"h"^2)/(4pi^2"m"^2"r"^2)`
`"Or,""r"=(("h"^2epsilon_o)/(pi"me"^2))"n"^2` ----------------------(4)
This equation gives the radius of the nth Bohr orbit.
`"For n"=1,"r"_1=(("h"^2epsilon_o)/(pi"me"^2))=0.537" ---------------(5)"`
`"In general,"" r"_n=(("h"^2epsilon_o)/(pi"me"^2))"n"^2`
The above equation gives the radius of Bohr orbit.
APPEARS IN
संबंधित 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
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]
Calculate the radius of Bohr’s fifth orbit for hydrogen atom
Explain, giving reasons, which of the following sets of quantum numbers are not possible.
(a) n = 0, l = 0, ml = 0, ms = + ½
(b) n = 1, l = 0, ml = 0, ms = – ½
(c) n = 1, l = 1, ml = 0, ms = + ½
(d) n = 2, l = 1, ml = 0, ms = – ½
(e) n = 3, l = 3, ml = –3, ms = + ½
(f) n = 3, l = 1, ml = 0, ms = + ½
Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.
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 radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits?
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.
if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:
a)`E_k = -E_p"/"2`
b) `E_k = -E_p`
c) `E_k = -2E_p`
d) `E_k = 2E_p`
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of the hydrogen atom.
State Bohr postulate of hydrogen atom that gives the relationship for the frequency of emitted photon in a transition.
Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
The difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.
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?
The Bohr radius is given by `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.
A beam of light having wavelengths distributed uniformly between 450 nm to 550 nm passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?
Radiation coming from transition n = 2 to n = 1 of hydrogen atoms falls on helium ions in n = 1 and n = 2 states. What are the possible transitions of helium ions as they absorbs energy from the radiation?
A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in ground state. (a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelengths may be observed in the transmitted beam? (b) A radiation detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelengths of radiation that may be detected by the detector.
Consider a neutron and an electron bound to each other due to gravitational force. Assuming Bohr's quantization rule for angular momentum to be valid in this case, derive an expression for the energy of the neutron-electron system.
According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.
Ratio of longest to shortest wavelength in Balmer series is ______.
Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.
The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-
The ratio of the ionization energy of H and Be+3 is ______.
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in nth orbit is proportional to `(1/"n")`.
Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.
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 ______.
The figure below is the Energy level diagram for the Hydrogen atom. Study the transitions shown and answer the following question:
- State the type of spectrum obtained.
- Name the series of spectrum obtained.
