Please show work, that would be really helpful Optical Spectroscopy: Calculate t

Question

Please show work, that would be really helpful

Optical Spectroscopy: Calculate the energy for the n = 3 electron orbit in the Hydrogen atom. Optical Spectroscopy: The diffraction grating on a optical spectroscope has 258 lines per mm so that s = 3876 mm. The turquoise line in the Hydrogen spectrum has a wavelength of lambda = 486 nm. What is the maximum order that this line can be viewed with the spectroscope? In other words, could you see this line in the first order spectrum, the second order, the third order, etc.? You may ignore the fact that the intensity of the lines decreases with as the order increases. (Hint: Since you cannot view any lines greater than 90 degrees set sin theta m = 1.) Optical Spectroscopy: What wavelength of light is emitted when a free electron is captured into the nf = 3 orbit of Hydrogen? Hint: What is the value of ni for a free (ionized) electron? Optical Spectroscopy: For an atomic transition in Hydrogen that emits visible light, the transition energy delta E should be approximately Optical Spectroscopy: What is the wavelength of the photon produced when an electron goes from the fifth (ni = 5) to the first (nf = 1) energy level in the Hydrogen atom? The ground state energy of Hydrogen is 13.6 eV.

Explanation / Answer

1. ni =2

1/L = R(1/n^2 -1/m^2)

1/L = 1.1e7 * (1/4-1/9)

L = 654 nm

option A it is
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2 option B
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3. 1/L = R(1/n^2 -1/m^2)

1/L = 1.1e7 * (1/25-1/))

L = 95 nm

opotion C
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4. En = 13.6 Z^2/n^2

E3 = -13.6/9 = -1.51 eV

option D
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apply d sin theta = m*L

m = (1/258 mm) *sin 90/486 nm

m =    8

option A it is

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