Advertisements
Advertisements
Question
In which of the following systems will the radius of the first orbit (n = 1) be minimum?
Options
Hydrogen atom
Deuterium atom
Singly ionized helium
Doubly ionized lithium
Advertisements
Solution
Doubly ionized lithium
For a hydrogen-like ion with Z protons in the nucleus, the radius of the nth state is given by
`rn = (n^2a_0)/Z`
Here , `a_0 = 0.53 " pm"`
For lithium,
Z = 3
Therefore, the radius of the first orbit for doubly ionised lithium will be minimum.
APPEARS IN
RELATED QUESTIONS
Find the wavelength of the electron orbiting in the first excited state in hydrogen atom.
What will be the energy corresponding to the first excited state of a hydrogen atom if the potential energy of the atom is taken to be 10 eV when the electron is widely separated from the proton? Can we still write En = E1/n2, or rn = a0 n2?
A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by
Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against ln(n)
(a) will pass through the origin
(b) will be a straight line with slope 4
(c) will be a monotonically increasing nonlinear curve
(d) will be a circle
Ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B. Let r, u, E and L represent the radius of the orbit, speed of the electron, energy of the atom and orbital angular momentum of the electron respectively. In ground state
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?
Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.
Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.
Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen?
In a hydrogen atom the electron moves in an orbit of radius 0.5 A° making 10 revolutions per second, the magnetic moment associated with the orbital motion of the electron will be ______.
Let En = `(-1)/(8ε_0^2) (me^4)/(n^2h^2)` be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it ______.
- it will not be absorbed at all.
- some of atoms will move to the first excited state.
- all atoms will be excited to the n = 2 state.
- no atoms will make a transition to the n = 3 state.
A hydrogen atom makes a transition from n = 5 to n = 1 orbit. The wavelength of photon emitted is λ. The wavelength of photon emitted when it makes a transition from n = 5 to n = 2 orbit is ______.
Which mathematical relation represents the energy of a photon emitted during an electronic transition from state ni to state nf?
What is the process called when an atom absorbs a photon whose energy exactly matches the energy required for an electronic transition?
In what year was Niels Bohr awarded the Nobel Prize in Physics for his explanation of the hydrogen atom spectrum?
What is the physical significance of Planck's constant (h) in the equation \[h\nu_{if} = E_{ni} - E_{nf}\]?
