Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given:
Distance travelled by the electron, d = 1.0 m
Wavelength of red light ,λ = 656.3 nm = 656.3 × 10^-9 m
Since the given wavelength lies in Balmer series, the transition that requires minimum energy is from n1 = 3 to n2 = 2.
Energy of this transition will be equal to the energy (E) that will be required for the transition from the ground state to n = 3.
`E_1 = 13.6 (1/n_1^2 1/n_2^2)`
`rArr E_1 = 13.6 (1 - 1/9)`
`= (13.6xx8)/9 = 12.09 eV`
Energy, E (eV) = 12.09 eV
∴ `V = 12.09 V`
Electric field, `E = V/d = 12.09/1 = 12.09 V//m`
∴ Minimum value of the electric field = 12.09 V/m = 12.1 V/m
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.
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?
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?
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 transitions will the wavelength be minimum?
The radius of the shortest orbit in a one-electron system is 18 pm. It may be
A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by
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
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
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
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.
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
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?
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).
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?
