Questions: Calculate the energy required for the electronic transition from n=3 to n=5 in the hydrogen atom.

Calculate the energy required for the electronic transition from n=3 to n=5 in the hydrogen atom.
Transcript text: Calculate the energy required for the electronic transition from $n=3$ to $\mathrm{n}=5$ in the hydrogen atom.
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Solution

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Solution Steps

Step 1: Understand the Energy Transition in a Hydrogen Atom

The energy levels of a hydrogen atom are given by the formula:

En=13.6eVn2 E_n = -\frac{13.6 \, \text{eV}}{n^2}

where n n is the principal quantum number, and 13.6 eV is the ionization energy of hydrogen.

Step 2: Calculate the Energy of Each Level

First, calculate the energy for n=3 n = 3 :

E3=13.6eV32=13.6eV9=1.5111eV E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} = -1.5111 \, \text{eV}

Next, calculate the energy for n=5 n = 5 :

E5=13.6eV52=13.6eV25=0.5440eV E_5 = -\frac{13.6 \, \text{eV}}{5^2} = -\frac{13.6 \, \text{eV}}{25} = -0.5440 \, \text{eV}

Step 3: Calculate the Energy Required for the Transition

The energy required for the transition from n=3 n = 3 to n=5 n = 5 is the difference between the energies of these two levels:

ΔE=E5E3=(0.5440eV)(1.5111eV)=0.9671eV \Delta E = E_5 - E_3 = (-0.5440 \, \text{eV}) - (-1.5111 \, \text{eV}) = 0.9671 \, \text{eV}

Final Answer

The energy required for the electronic transition from n=3 n = 3 to n=5 n = 5 in the hydrogen atom is 0.9671eV\boxed{0.9671 \, \text{eV}}.

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