Question

1. Using the Balmer formula calculate the first four wavelengths of the spectrum corresponding to n=3,4,5, and 6. Show your work.

2. Describe the possible orbits of an electron in a hydrogen atom that are allowed by the Bohr thoery.

3. What is the stationary state of the atom in Bohr theory?

Answer 1

Answer 1)

By Balmer's formula

1/L = R * ( 1/4 - 1/n²) where n = 3,4,5,6......

For n=3

1/L = 109677 * (1/4 - 1/9) = 15232.91 cm^-1where R = Rydberg's constant

or L = 6.56 * 10^-5 cm = 656.3 nm
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n=4
1/L = 109677 * (1/4 - 1/16) cm^-1

or L = 486.1 nm
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n=5

1/L = 109677 * (1/4 - 1/25) cm^-1

or L = 434.1 nm
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n=6

1/L = 109677 * (1/4 - 1/36) cm^-1

or L = 410.2 nm

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Answer b)

In hydrogen atom Bohr's theory:
1. Electrons can only be present in certain orbits at particular set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels.
2. Electrons can gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency f determined by the energy difference of the levels according to the Planck relation E = hf where h is Planck's constant.
3. The energy content of each orbit = -13.6/n² eV where n is principal quantum number.

So, electrons occupy orbits whose energy content are values of form -13.6/n² eV , n = 1,2,3,4......

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Answer c)

Stationary states:
The electrons are present only at particular set of distances from the nucleus and with particular energy content goverened by equation E_n = -13.6/n² eV , n = 1,2,3,4...... In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics.
These orbits are called as stationary states.