Advertisements
Advertisements
प्रश्न
Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number n changes by 2. (a) Find the smallest wavelength emitted by hydrogen. (b) List the wavelength emitted by hydrogen in the visible range (380 nm to 780 nm).
उत्तर
Given:
Possible transitions:
From n1 = 1 to n2 = 3
n1 = 2 to n2 = 4
(a) Here, n1 = 1 and n2 = 3
Energy, `E = 13.6 (1/n_1^2- 1/n_2^2)`
`E = 13.6 (1/1 - 1/9)`
`= 13.6xx8/9 ....... (i)`
Energy (E) is also given by
`E = (hc)/lamda`
Here, h = Planck constant
c = Speed of the light
λ = Wavelength of the radiation
`therefore E = (6.63xx10^-34xx3xx10^2)/lamda` ........(i)
`"Equanting equation (1) and (2) , we have"`
`lamda = (6.63xx10^-34xx3xx10^8xx9)/(13.6xx8)`
= 0.027 × 10-7 = 103 nm
(b) Visible radiation comes in Balmer series.
As 'n' changes by 2, we consider n = 2 to n = 4.
`"Energy" , E_1 = 13.6 (1/n_1^2 - 1/n_2^2)`
= `13.6 xx (1/4 - 1/16)`
=2.55 eV
If `lamda_1` is the wavelength of the radiation, when transition takes place between quantum number n = 2 to n = 4, then
`255 = 1242/lamda_1`
or λ1 = 487 nm
APPEARS IN
संबंधित प्रश्न
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?
In which of the following transitions will the wavelength be minimum?
As one considers orbits with higher values of n in a hydrogen atom, the electric potential energy of the atom
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.
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
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 state n = 6 makes two successive transitions and reaches the ground state. In the first transition a photon of 1.13 eV is emitted. (a) Find the energy of the photon emitted in the second transition (b) What is the value of n in the intermediate state?
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?
A gas of hydrogen-like ions is prepared in a particular excited state A. It emits photons having wavelength equal to the wavelength of the first line of the Lyman series together with photons of five other wavelengths. Identify the gas and find the principal quantum number of the state A.
A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength 50 nm. Assuming that the entire photon energy is taken up by the electron with what kinetic energy will the electron be ejected?
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?
When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n = 3 to n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.
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 the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.
