The energy levels of a hydrogen atom are given by the formula:
En=−13.6 eVn2 E_n = -\frac{13.6 \, \text{eV}}{n^2} En=−n213.6eV
where n n n is the principal quantum number, and 13.6 eV is the ionization energy of hydrogen.
First, calculate the energy for n=3 n = 3 n=3:
E3=−13.6 eV32=−13.6 eV9=−1.5111 eV E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} = -1.5111 \, \text{eV} E3=−3213.6eV=−913.6eV=−1.5111eV
Next, calculate the energy for n=5 n = 5 n=5:
E5=−13.6 eV52=−13.6 eV25=−0.5440 eV E_5 = -\frac{13.6 \, \text{eV}}{5^2} = -\frac{13.6 \, \text{eV}}{25} = -0.5440 \, \text{eV} E5=−5213.6eV=−2513.6eV=−0.5440eV
The energy required for the transition from n=3 n = 3 n=3 to n=5 n = 5 n=5 is the difference between the energies of these two levels:
ΔE=E5−E3=(−0.5440 eV)−(−1.5111 eV)=0.9671 eV \Delta E = E_5 - E_3 = (-0.5440 \, \text{eV}) - (-1.5111 \, \text{eV}) = 0.9671 \, \text{eV} ΔE=E5−E3=(−0.5440eV)−(−1.5111eV)=0.9671eV
The energy required for the electronic transition from n=3 n = 3 n=3 to n=5 n = 5 n=5 in the hydrogen atom is 0.9671 eV\boxed{0.9671 \, \text{eV}}0.9671eV.
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