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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 ______.
विकल्प
`8/7lambda`
`16/7lambda`
`24/7lambda`
`32/7lambda`
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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.
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