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NCERT Class XI Chemistry Structure of Atom Solutions

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Question : 16 of 67
Marks: +1, -0
(i) The energy associated with the first orbit in the hydrogen atom is –2.18 × 10−18 J atom−110^{-18}\,\mathrm{J}\,\mathrm{atom}^{-1}. What is the energy associated with the fifth orbit?
(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
Solution:  
(i) Energy associated with nth orbit in hydrogen atom is
EnE_n = −2.18×10−18n2 J atom−1\frac{-2.18\times10^{-18}}{n^2}\,\mathrm{J}\,\mathrm{atom}^{-1}
∴ Energy associated with 5th orbit is
E5E_5 = −2.18×10−1852\frac{-2.18\times10^{-18}}{5^2} = - 8.72 × 10−20 J atom−110^{-20}\,\mathrm{J}\,\mathrm{atom}^{-1}
(ii) Radius of Bohr’s fifth orbit for hydrogen atom, rn = 0.529 n2 Å
r5r_5 = 0.529 × 525^2 Å
r5r_5 = 13.225 Å = 13.225 × 10−1010^{-10} m [Since 1 Å = 10−1010^{-10} m]
= 1.3225 × 10−910^{-9} m = 1.3225 nm [Since 1 nm = 10−910^{-9} m]
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