Advertisements
Advertisements
प्रश्न
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
Advertisements
उत्तर
For He+ ion,
Atomic number, Z = 2
For hydrogen like ions, radius (r) of the nth state is given by
`r = (0.53 n^2)/ZÅ`
Here
Z= Atomic number of ions
n = Quantum number of the state
Energy (E) of the nth state is given by
`E_n = -(13.6 Z^2)/(n^2)`
(a)
for n = 1
Radius,
`r = (0.53xx(1)^2)/2`
`Å = 0.265 A^0`
Energy, En = `(-13.6 xx 4)/1`
= - 54.4 ev
(b)
For n = 4,
Radius, `r = (0.53xx16)/2 = 4.24 Å `
Energy, `E = (-13.6xx4)/16= -3.4 eV`
(c)
For n = 10,
`Radius, r = (0.53xx100)/2`
= 26.5 Å
Energy, E = `(-13.6 xx 4 )/100 = -0.544 eV`
APPEARS IN
संबंधित प्रश्न
Find the wavelength of the electron orbiting in the first excited state in 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?
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?
The minimum orbital angular momentum of the electron in a hydrogen atom is
In which of the following transitions will the wavelength be minimum?
Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of trincipal quantum number n?
As one considers orbits with higher values of n in a hydrogen atom, the electric potential energy of the atom
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
Calculate the smallest wavelength of radiation that may be emitted by (a) hydrogen, (b) He+ and (c) Li++.
A group of hydrogen atoms are prepared in n = 4 states. List the wavelength that are emitted as the atoms make transitions and return to n = 2 states.
A hydrogen atom in a state having a binding energy of 0.85 eV makes transition to a state with excitation energy 10.2 e.V (a) Identify the quantum numbers n of the upper and the lower energy states involved in the transition. (b) Find the wavelength of the emitted radiation.
Whenever a photon is emitted by hydrogen in Balmer series, it is followed by another photon in Lyman series. What wavelength does this latter photon correspond to?
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 maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
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.
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.
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.
