434.1 nm 410.1 nm | 486.1 nm 656.3 nm H 400 450 500 550 600 650 700 750 nm Prism Gas Slit discharge tube containing hydrogen A Visible spectrum 1 (nm) 400 450 500 550 600 650 700 750 nm Hg 400 450 500 550 600 650 700 750 nm Sr 400 450 500 550 600 650 700 750 nm B

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Chapter19: Astrobiology: Life On Other Worlds
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The quantum-mechanical treatment of the hydrogen atomgives the energy, E, of the electron as a function of the principal quantum number, n:E=-h²/8π²mₑ²aₒ²n² (n=123...) where his Planck’s constant, meis the electron mass, and a0 is 52.92X10⁻¹² =-m.(a) Write the expression in the form E(constant)=-(constant)1/n² , evalu-ate the constant (in J), and compare it with the corresponding expression from Bohr’s theory.(b) Use the expression to find ΔE between n=2 and n=3.(c) Calculate the wavelength of the photon that corresponds tothis energy change. Is this photon seen in the hydrogen spectrumobtained from experiment

434.1 nm
410.1 nm |
486.1 nm
656.3 nm
H
400
450
500
550
600
650
700
750 nm
Prism
Gas
Slit
discharge
tube
containing
hydrogen
A
Visible
spectrum
1 (nm)
400
450
500
550
600
650
700
750 nm
Hg
400
450
500
550
600
650
700
750 nm
Sr
400
450
500
550
600
650
700
750 nm
B
Transcribed Image Text:434.1 nm 410.1 nm | 486.1 nm 656.3 nm H 400 450 500 550 600 650 700 750 nm Prism Gas Slit discharge tube containing hydrogen A Visible spectrum 1 (nm) 400 450 500 550 600 650 700 750 nm Hg 400 450 500 550 600 650 700 750 nm Sr 400 450 500 550 600 650 700 750 nm B
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