The ionization energy of a hypothetical atom is 50 eV . If this atom obeys Bohr’s atomic model,the energy of electron in its fifth orbit will be?
Question
The ionization energy of a hypothetical atom is 50 eV . If this atom obeys Bohr’s atomic model,the energy of electron in its fifth orbit will be?
Solution
Sure, let's solve this step by step.
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First, we need to understand that the ionization energy is the energy required to remove an electron from the ground state (n=1) of an atom. In this case, the ionization energy is given as 50 eV.
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According to Bohr's model, the energy of an electron in the nth orbit of an atom is given by the formula: E = -13.6/n^2 eV, where n is the number of the orbit.
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We know that the energy of the electron in the ground state (n=1) is equal to the ionization energy, so we can set up the equation: -13.6/1^2 = -50 eV.
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Solving this equation, we find that the energy of the electron in the ground state is -50 eV.
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Now, we want to find the energy of the electron in the fifth orbit (n=5). We can use the same formula: E = -13.6/n^2 eV.
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Substituting n=5 into the equation, we get: E = -13.6/5^2 eV = -13.6/25 eV = -0.544 eV.
So, the energy of the electron in its fifth orbit is -0.544 eV.
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