Question

the de Broglie wavelength of the electron in a certain bohr orbit of hydrogen atom is 9.985 angstrum. what is the quantum number of the bohr orbit​

Answer 1

Answer:

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Answer 2

Concept:

The de Broglie wavelength formula compares the characteristics of waves and particles. Quantum mechanics includes the de Broglie wavelength. The de Broglie wavelength expresses the likelihood of discovering the object at a particular configuration space point.

Given:

The wavelength of the electron (λ) = 9.985 Angstrom or  Å = 9.985 x 10⁻¹⁰  m

Find:

What is the quantum number of the Bohr orbit​?

Solution:

We know that the wavelength of an electron can be expressed as:

                                      2πrn = λ

where λ is the wavelength of an electron.

r is the radius of the hydrogen atom.

n is the quantum number.

By substituting the given values in the above expression we get the value of n as follows below,

            2 x 3.14 x 5.13 x 10⁻¹¹ x n =  9.985 x 10⁻¹⁰

                                                    n = 9.985 x 10⁻¹⁰ / (2 x 3.14 x 5.13 x 10⁻¹¹)

                                                    n = 0.3099 x 10

                                                    n = 3.099

                                                    n = 3

Hence, the quantum number of the Bohr orbit​ is 3.

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