Advertisements
Advertisements
प्रश्न
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 ______.
पर्याय
`8/7lambda`
`16/7lambda`
`24/7lambda`
`32/7lambda`
Advertisements
उत्तर
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 `underlinebb(32/7lambda)`.
Explanation:
Given: n1 = 5, n2 = 1, Z = 1 and λ is wavelength of the wave, R is the Rydberg constant i.e. 1.097 × 107 m-1 and Z is the atomic number of the element. ni is lower energy level and nh is the higher energy level.
Calculating the wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 5 to n = 1 state,
`1/lambda = RZ^2(1/(n_i^2) - 1/(n_h^2))`
⇒ `lambda = RZ^2(1/1^2 - 1/5^2)`
⇒ `lambda = 24/25RZ^2`
⇒ `RZ^2 = (25lambda)/24` ...(i)
Calculating the wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 5 to n = 2 state,
`1/lambda^' = RZ^2(1/n_i^2 - 1/n_h^2)`
`1/lambda^' = RZ^2(1/2^2 - 1/5^2)`
= `RZ^2 xx 21/100`
⇒ `1/lambda^' = (25lambda)/24 xx 21/100` ...[From (i)]
= `32/7 lambda`
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?
When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.
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?
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
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?
Why do only discrete frequencies appear in atomic emission spectra?
What is the process called when an atom absorbs a photon whose energy exactly matches the energy required for an electronic transition?
What is a key limitation of continuous spectra that is resolved by the observation of discrete emission lines?
