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.
Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?
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
(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
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?
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?
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.
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.
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?
