The energy associated with the first orbit in the hydrogen atom is - 2.18 x 10^-18J atom^-1. What is the energy associated with the fifth orbit?

(ii) Calculate the radius of Bohr’s fifth orbit for the hydrogen atom.

Solution

The energy E_n of an electron in an orbit n is given by

straight E subscript straight n space equals space minus fraction numerator 2.17 space cross times space 10 to the power of negative 18 end exponent over denominator straight n squared end fraction atm to the power of negative 1 end exponent Here space straight n space equals space 5 therefore space space space space straight E subscript 5 space equals space fraction numerator negative 2.17 space cross times space 10 to the power of negative 18 end exponent straight J over denominator left parenthesis 5 right parenthesis squared end fraction atm to the power of negative 1 end exponent equals space fraction numerator negative 2.17 space cross times space 10 to the power of negative 18 end exponent straight J over denominator 25 end fraction equals space minus 8.68 space cross times space 10 to the power of negative 20 end exponent straight J

ii) Radius of Bohr’s n^th orbit for hydrogen atom is given by,

r_n =(0.0529)n²

For

n=5

r_s=0.0529nm x 5 x5

r_s =1.3225nm

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