Question

4.66 Explain how the Bohr model of the atom accounts for the existence of atomic line spectra. 167 TATI. .

Answer 1

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ANSWER - Q 4.66:

• Atomic line spectra

This type of spectra show only radiation of specific wavelengths. The hydrogen line spectra shows 4 lines in the visible region: 410 nm (violet), 434 nm ( blue), 486 nm (blue-green) and 656 (red).

• Bhor model of atoms

According the Bhor model of atom, the electrons moves around the nucleus and they are placed in specific orbits (which contains a definite energy and certain allowed radii). This means that electron only occupy specific regions of space.

• Explanation of line spectra using the Bhor model of atom

According to Bhor model of atom, electrons only could move from one allowed energy level (orbit) to another allowed energy level and this movement cause a definite absorption or emission of energy (Bhor use the definition of energy proposed by Planck: E = hv).

• If electron jumps from a lower orbit to a higher orbit, the electrons absorbs energy to jump
• If electron jumps from a higher orbit to a lower orbit, the electrons emits energy to jump

The radiation of the electron jumps are the lines observed in the atomic spectra lines because, the energy of each jump is defined as

$\Delta E=-2.18x10^{-18}\, J\times \left ( \frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}} \right )$

where n_f = final energy level and n_i = initial energy level

at the same time, the energy of the electron jump is defined as

$\Delta E=\frac{hc}{\lambda }$

Then,

$\Delta E=-2.18x10^{-18}\, J\times \left ( \frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}} \right )=\frac{hc}{\lambda }$

Thus, the wavelength of each line in the line spectra is due to the jump of an electron from one orbit to other orbit