Advertisements
Advertisements
प्रश्न
Taking the Bohr radius as a0 = 53 pm, the radius of Li++ ion in its ground state, on the basis of Bohr’s model, will be about ______.
पर्याय
53 pm
27 pm
18 pm
13 pm
Advertisements
उत्तर
Taking the Bohr radius as a0 = 53 pm, the radius of Li++ ion in its ground state, on the basis of Bohr’s model, will be about 18 pm.
Explanation:
Bohr’s radius of orbit (for Hydrogen and H,-like atoms): For an electron around a stationary nucleus, the electrostatic force of attraction provides the necessary centripetal force.
i.e., `1/(4πε_0) ((Ze)e)/r^2 = (mv^2)/r` ......(i)
Also `mvr = (nh)/(2pi)` ......(ii)
From equations (i) and (ii), the radius of nth orbit
`r_n = (n^2h^2)/(4pi^2 kZme^2) = (n^2h^2ε_0)/(pimZe^2) = 0.53 n^2/Z Å` ......`(k = 1/(4πε_0))`
⇒ `r_n ∝ n^2/Z` or `r_n ∝ 1/Z`
`r_n = a_0 n^2/Z`, where a0 = the Bhor radius = 53 pm
‘The atomic number (Z) of lithium is 3.
As `r_n = a_0 n^2/Z`,
Therefore, the radius of Li++ ion in its ground state, on the basis of Bohr’s model. will be about `1/3` times to that of Bohr's radius.
Therefore, the radius of lithium ion is near r = `53/3` = 18 pm.
APPEARS IN
संबंधित प्रश्न
Using Bohr's postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr's radius.
In Bohr’s model of the hydrogen atom, the radius of the first orbit of an electron is r0 . Then, the radius of the third orbit is:
a) `r_0/9`
b) `r_0`
c) `3r_0`
d) `9r_0`
Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf).
When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2, 1, identify the spectral series to which the emission lines belong.
Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states tan be expressed as the sum of kinetic energy (K) and potential energy (U), where K = −2U. Hence deduce the expression for the total energy in the nth energy level of hydrogen atom.
Write the expression for Bohr’s radius in hydrogen atom ?
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?
Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal?
Calculate angular momentum of an electron in the third Bohr orbit of a hydrogen atom.
Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.
The ratio of the ionization energy of H and Be+3 is ______.
An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state ______.
- the electron would not move in circular orbits.
- the energy would be (2)4 times that of a H-atom.
- the electrons, orbit would go around the protons.
- the molecule will soon decay in a proton and a H-atom.
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")`.
Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to:
The first ionization energy of H is 21.79 × 10-19 J. The second ionization energy of He atom is ______ × 10-19J.
What is the energy associated with first orbit of Li2+ (RH = 2.18 × 10-18)?
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 ______.
According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.
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.
The de Broglie wavelength of an electron in the first Bohr’s orbit of hydrogen atom is equal to ______.
