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Question:

The energy associated with the first orbit in the hydrogen atom is 2.18×10⁻¹⁸ J/atom. What is the energy associated with the fifth orbit?

Solution:

(i)The expression for the energy associated with the nth orbit in a hydrogen atom is En = -2.17×10⁻¹⁸/n² J/atom. The energy associated with the fifth orbit is En = -2.17×10⁻¹⁸/5² J/atom = -8.68×10⁻²⁰ J (ii) The radius of Bohr's nth orbit is given by the expression rn = 0.0529n² nm. For the fifth orbit, the radius is r5 = 0.0529 × 5² nm = 1.3225 nm.