Question

What is the ratio of energy difference between Bohr's first orbit and second orbit,and that of between third and second orbit ?

Answer 1

Answer on Question #47490 - Chemistry - Inorganic Chemistry

What is the ratio of energy difference between Bohr's first orbit and second orbit, and that of between third and second orbit?

Answer:

The energy of an electron in Bohr's orbit of hydrogen atom is given by the expression:

$$E _ {n} = - \frac {2 \pi^ {2} m e ^ {4} Z ^ {2}}{n ^ {2} h ^ {2} \left(4 \pi \varepsilon_ {0}\right) ^ {2}} = - 13.6 \frac {Z ^ {2}}{n ^ {2}} e V$$

As an example when it is an atom of hydrogen $Z = 1$ for hydrogen and above equation can be further simplified to:

$$E _ {n} = - 13.6 / n ^ {2} e V$$

The energies of electrons in the Bohr's orbits of hydrogen atom expressed in eV are:

Excited state(s) represent $n = 2, 3, 4$ ... (greater than 1).

The ratio of energy of electrons in the orbits of hydrogen atom is:

$$E _ {1}: E _ {2}: E _ {3}: E _ {4} \dots \dots \dots = 1 / 1 ^ {2}: 1 / 2 ^ {2}: 1 / 3 ^ {2}: 1 / 4 ^ {2} \dots \dots \dots = 1: 1 / 4: 1 / 9: 1 / 16 \dots \dots$$

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