Advertisements
Advertisements
Question
The radius of the shortest orbit in a one-electron system is 18 pm. It may be
Options
hydrogen
deuterium
He+
Li++
Advertisements
Solution
Li++
The radius of the nth orbit in one electron system is given by
`r_n = (n^2a_0)/Z`
Here, a0 = 53 pm
For the shortest orbit,
n = 1
For hydrogen,
Z = 1
∴ Radius of the first state of hydrogen atom = 53 pm
For deuterium,
Z= 1
∴ Radius of the first state of deuterium atom = 53 pm
For He+,
Z = 2
∴ Radius of He+ atom =`53/2 pm = 26.5 "pm"`
For Li++,
Z = 3
∴ Radius of Li++ atom = `53/3 "pm" = 17.66"pm" ≈ 18 "pm"`
The given one-electron system having radius of the shortest orbit to be 18 pm may be Li++.
The given one-electron system having radius of the shortest orbit to be 18 pm may be Li++.
APPEARS IN
RELATED QUESTIONS
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
If Bohr’s quantisation postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
Find the wavelength of the electron orbiting in the first excited state in hydrogen atom.
The first excited energy of a He+ ion is the same as the ground state energy of hydrogen. Is it always true that one of the energies of any hydrogen-like ion will be the same as the ground state energy of a hydrogen atom?
Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?
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
Calculate the smallest wavelength of radiation that may be emitted by (a) hydrogen, (b) He+ and (c) Li++.
Find the binding energy of a hydrogen atom in the state n = 2.
A hydrogen atom emits ultraviolet radiation of wavelength 102.5 nm. What are the quantum numbers of the states involved in the transition?
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
Average lifetime of a hydrogen atom excited to n = 2 state is 10−8 s. Find the number of revolutions made by the electron on the average before it jumps to the ground state.
Consider an excited hydrogen atom in state n moving with a velocity υ(ν<<c). It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency ν of the emitted radiation. Compare this with the frequency ν0 emitted if the atom were at rest.
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 ______.
The Balmer series for the H-atom can be observed ______.
- if we measure the frequencies of light emitted when an excited atom falls to the ground state.
- if we measure the frequencies of light emitted due to transitions between excited states and the first excited state.
- in any transition in a H-atom.
- as a sequence of frequencies with the higher frequencies getting closely packed.
Positronium is just like a H-atom with the proton replaced by the positively charged anti-particle of the electron (called the positron which is as massive as the electron). What would be the ground state energy of positronium?
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 ______.
