(i) The energy associated with first orbit in hydrogen atom is –2.17 × 10-18 J atom-1. What is the energy associated with the fifth orbit?
(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
(i) The energy associated with first orbit in hydrogen atom is –2.17 × 10-18 J atom-1. What is the energy associated with the fifth orbit?
(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
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1 Answer
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(i) For an electron, the energies in the two orbits can be compared as:
E1 / E2 = (n2 / n1)2 [Since E is inversely proportional to n2]
Given: n1 = 1, E1 = –2.17 × 10-18 J atom-1, n2 = 5
Therefore, (–2.17 × 10-18 J atom-1) / E2 = (5 / 1) 2 = 25
=> E2 = (–2.17 × 10-18 J atom-1) / 25 = –8.77 x 10-20 J atom-1
(ii) For hydrogen atom; rn = 0.529 x n2 Å
r5 = 0.529 x (5)2 = 13.225 Å = 1.3225 nm.
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