The wavelength of radiation required to remove the electron of hydrogen atom from n=2 orbit to n=-∞ is?

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Wavelength of Radiation Required to Remove Electron from Hydrogen Atom

Hydrogen atom consists of one proton and one electron. The electron revolves around the proton in different energy levels or orbits. The energy of the electron is quantized, i.e., it can only have certain discrete values. When an electron absorbs a photon, it can jump from a lower energy level to a higher energy level. Similarly, when an electron emits a photon, it can jump from a higher energy level to a lower energy level.

Energy Levels of Hydrogen Atom

The energy levels of a hydrogen atom are given by the formula:

E_n = -13.6/n² eV

where n is an integer and E_n is the energy of the nth energy level. The energy levels are arranged in such a way that the energy of the electron decreases as the value of n increases.

Transition of Electron from n=2 to n=-∞

The wavelength of radiation required to remove the electron from the n=2 orbit to n=-∞ is the wavelength of the photon emitted when the electron jumps from n=2 to n=-∞. When the electron jumps from n=2 to n=-∞, it emits a photon of a certain wavelength. The energy of the photon is equal to the difference in energy between the two energy levels:

E₂ - E_-∞ = -13.6/2² - 0 = -3.4 eV

where E₂ is the energy of the n=2 level and E_-∞ is the energy of the electron when it is completely removed from the atom.

Calculation of Wavelength

The energy of a photon is given by the formula:

E = hc/λ

where h is the Planck's constant (6.626 x 10^-34 J s), c is the speed of light (3 x 10⁸ m/s), and λ is the wavelength of the photon.

Substituting the values, we get:

λ = hc/E = (6.626 x 10^-34 J s x 3 x 10⁸ m/s)/(-3.4 eV x 1.602 x 10^-19 J/eV) = 1.21 x 10^-7 m

Therefore, the wavelength of radiation required to remove the electron from the n=2 orbit to n=-∞ is 1.21 x 10^-7 m.

Answer

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