Hydrogen atoms are excited by a laser to the ?=4 state and then allowed to emit.What is the maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system?57284316Calculate the wavelength of the 4⟶1 transition.?=__________m

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Asked Oct 27, 2019
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Hydrogen atoms are excited by a laser to the ?=4 state and then allowed to emit.

What is the maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system?

5

7

2

8

4

3

1

6

Calculate the wavelength of the 4⟶1 transition.

?=__________m

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Expert Answer

Step 1

Given, n = 4

The maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system can be calculated as:

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n(n-1) Number of spectral lines 2 4(4-1) 6 Number of spectral lines 2

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Step 2

The Rydberg equation for the calculation of the wavelength of an atomic element when an excited electron moves from the quantum shells is expressed as:

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1 nf2 λ ni2 Where, wavelength R Rydberg constant = 1.097 x 107 m1 nf the principal quantum number of the final energy level of an electron the principal quantum number of the initial energy level of an electron ni

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Step 3

Given, 4⟶1 transition

nf = 1

ni = 4

Therefore, wavelength of the spec...

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1 1 = R ( 'nf2 1 ni2 1 1.097 x 107 m1 λ 12 42 1 10284375 m1 λ 1 λ- 10284375 m-1 =9.7235 x 10-8 m

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