The ratio of the kinetic energy to the total energy of an electron in Bohr orbit is
- 1 : -1
- - 1 : 1
- 1 : 2
- 2 : -1
The Correct Option is A
Solution and Explanation
P.E. of electron in Bohr orbit, P.E. = - $\frac{ke^2}{r}$
$\therefore$ Total energy, E = K.E. + P.E = $\frac{1}{2} \frac{ke^2}{r} - \frac{ke^2}{r} = -\frac{1}{2} \frac{ke^2}{r}$
$\therefore$ $\frac{K.E.}{E} = \frac{\frac{1}{2} ke^2}{- \frac{1}{2} ke^2} = \frac{1}{-1}$
$\therefore$ K.E. : E = 1: -1
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Concepts Used:
Atomic Spectra
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states.
Read More: Atomic Spectra
Spectral Series of Hydrogen Atom
Rydberg Formula:
The Rydberg formula is the mathematical formula to compute the wavelength of light.
\[\frac{1}{\lambda} = RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})\]Where,
R is the Rydberg constant (1.09737*107 m-1)
Z is the atomic number
n is the upper energy level
n’ is the lower energy level
λ is the wavelength of light
Spectral series of single-electron atoms like hydrogen have Z = 1.
Uses of Atomic Spectroscopy:
- It is used for identifying the spectral lines of materials used in metallurgy.
- It is used in pharmaceutical industries to find the traces of materials used.
- It can be used to study multidimensional elements.