Advertisements
Advertisements
प्रश्न
In which of the following transitions will the wavelength be minimum?
विकल्प
n = 5 to n = 4
n = 4 to n = 3
n = 3 to n = 2
n = 2 to n = 1
Advertisements
उत्तर
n = 2 to n = 1
For the transition in the hydrogen-like atom, the wavelength of the emitted radiation is calculated by
`1/lamda = RZ^2 (1/n^1 - 1/n^2)`
Here, R is the Rydberg constant.
For the transition from n = 5 to n = 4, the wavelength is given by
`1/lamda = RZ^2 (1/4^2 - 1/5^2)`
`lamda = 400/(9RZ^2)`
For the transition from n = 4 to n = 3, the wavelength is given by
`1/lamda = RZ^2 (1/3^2 - 1/4^2)`
`lamda = (144)/ (7RZ^2)`
For the transition from n = 3 to n = 2, the wavelength is given by
`1/lamda = RZ^2 (1/2^2 - 1/3^2 )`
`lamda = (36)/(5RZ^2)`
For the transition from n = 2 to n = 1, the wavelength is given by
`1/lamda = RZ^2 (1/2^2 - 1/3^2)`
`lamda = 2/(RZ^2)`
From the above calculations, it can be observed that the wavelength of the radiation emitted for the transition from n = 2 to n = 1 will be minimum.
APPEARS IN
संबंधित प्रश्न
Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, a thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10−10 m).
(a) Construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.
(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.
Find the wavelength of the electron orbiting in the first excited state in hydrogen atom.
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.
In which of the following systems will the radius of the first orbit (n = 1) be minimum?
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) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
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.
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.
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 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?
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 ______.
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?
