Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
There will be three wavelengths.
(i) For the transition from (n = 4) to (n = 3) state
(ii) For the transition from (n = 3) to (n = 2) state
(iii) For the transition from (n = 4) to (n = 2) state
Let `(lamda_1)` be the wavelength when the atom makes transition from (n = 4) state to (n = 2) state.
Here,
n1 = 2
n2 = 4
Now, the wavelength `(lamda_1)` will be
`1/lamda_1 = R (1/n_1^2 - 1/n_2^2)`
`R = 1.097 xx 10^7 m^-1`
`1/lamda_1 = 1.097xx 10^7 xx (1/4 - 1/16)`
`rArr 1/lamda_1 = 1.097 xx 10^7 ((4-1)/(16))`
`rArr 1/lamda_1 = (1.097xx10^7xx3)/16`
`rArr lamda_1 = (16xx10^-7)/(3xx1.097)`
= 4.8617 × 10-7
= 486.1 × 10-9
= 487 nm
When an atom makes transition from (n = 4) to (n = 3), the wavelength (λ2) is given by
Here again
`n_1 = 3`
`n_2 = 4`
`1/lamda_2 = 1.097 xx 10^7 (1/9 - 1/16)`
`rArr 1/lamda_2 = 1.097 xx 10^7 ((16 -9)/144)`
`rArr 1/lamda_2 = (1.097xx 10^7 xx 7)/144`
`rArr lamda_2 = 144/(1.097 xx 10^7 xx 7)`
= 1875 nm
Similarly, wavelength (λ2) for the transition from (n = 3) to (n = 2) is given by
When the transition is n1 = 2 to n2 = 3:
`1/lamda_3 = 1.097 xx 10^7 (1/4 - 1/9)`
`rArr 1/lamda_3 = 1.097 xx 10^7 ((9-4)/36) `
`rArr 1/lamda_3 = (1.097xx10^7)/36`
`rArr lamda_3 = (36xx10^7xx5)/36`
`rArr lamda_3 = (36xx10^7)/((1.097)xx5) = 656 nm`
APPEARS IN
संबंधित प्रश्न
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
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?
In which of the following transitions will the wavelength be minimum?
Which of the following products in a hydrogen atom are independent of the principal quantum number n? The symbols have their usual meanings.
(a) vn
(b) Er
(c) En
(d) vr
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?
(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
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.
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?
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.
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.
A hydrogen atom moving at speed υ collides with another hydrogen atom kept at rest. Find the minimum value of υ for which one of the atoms may get ionized.
The mass of a hydrogen atom = 1.67 × 10−27 kg.
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.
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?
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.
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 ______.
