The energy of transition of an electron from 5th to the 3rd Bohr orbit of a hydrogen atom
1/wavelength = R(1/9 - 1/25)
Then E = hc/wavelength.
OR
E = 2.18E-18(1/9 - 1/25)
To calculate the energy of the transition of an electron from one Bohr orbit to another in a hydrogen atom, we can use the formula:
ΔE = - (13.6 eV) * (Z^2 / n_f^2 - Z^2 / n_i^2)
Where:
- ΔE is the energy difference (in electron volts, eV) between the final (n_f) and initial (n_i) orbits
- Z is the atomic number, which is 1 for hydrogen
In this case, the electron is transitioning from the 5th (n_i = 5) to the 3rd (n_f = 3) Bohr orbit of the hydrogen atom. Plugging these values into the formula, we have:
ΔE = - (13.6 eV) * (1^2 / 3^2 - 1^2 / 5^2)
Simplifying the equation, we get:
ΔE = - (13.6 eV) * (1/9 - 1/25)
= - (13.6 eV) * (16-9) / (225)
= - (13.6 eV) * (7/225)
= - (13.6 eV * 7) / 225
= - 0.424 eV
Therefore, the energy of transition from the 5th to the 3rd Bohr orbit of a hydrogen atom is approximately -0.424 eV. The negative sign indicates that energy is released during the transition.