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A hydrogen – like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels both these values). (a) Find the atomic number of the atom. (b) Calculate the smallest wavelength emitted in these transitions. (Take hc = 1240 eV-nm, ground state energy of hydrogen atom = -13.6 eV)

A hydrogen – like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels both these values). 
(a) Find the atomic number of the atom.
(b) Calculate the smallest wavelength emitted in these transitions.
(Take hc = 1240 eV-nm, ground state energy of hydrogen atom = -13.6 eV)

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Hello Student,
Please find the answer to your question
(a) If x is the difference in quantum number of the states than x+1C2 = 6 ⇒ x = 3
Now, we have –z2 (13.6eV) / n2 = - 0.85eV …(i)
And –z2 (13.6 eV) / (n + 3)2 = - 0.544 eV …(ii)
Solving (i) and (ii) we get n = 12 and z = 3
(b) Smallest wavelength λ is given by
hc / λ = (0.85 – 0.544) eV
Solving, we get λ = 4052 nm.
Thanks
Navjot Kalra
askIITians Faculty

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