The number of possible lines of Paschen series when electron jumps from 7th excited state toground state in hydrogen like atom is :Correct answer is '5'. Can you explain this answer?

Question

Answer

Explanation:

Paschen series is a set of spectral lines in the infrared region of the hydrogen spectrum that corresponds to transitions from higher energy levels to the third energy level of hydrogen atom. The formula for the calculation of the wavelength of the Paschen series is given by:

Wavelength = 1.097 x 10^-7 m * [(1/3^2) - (1/n^2)]

where n is the energy level of the electron.

To calculate the number of possible lines of Paschen series when the electron jumps from the 7th excited state to the ground state, we need to find all the possible values of n for which the wavelength falls in the infrared region.

Steps to calculate the number of possible lines:

Calculate the wavelength for n = 3, 4, 5, 6, and 7 using the above formula.

Check if the wavelength falls in the infrared region, which is between 700 nm and 1 mm.

If the wavelength falls in the infrared region, count it as a possible line of Paschen series.

The number of possible lines is the total number of wavelengths that fall in the infrared region.

Calculations:

For n=3, the wavelength is 656.3 nm, which falls in the visible region and is not a possible line of Paschen series.

For n=4, the wavelength is 1875 nm, which falls in the infrared region and is a possible line of Paschen series.

For n=5, the wavelength is 1282 nm, which falls in the infrared region and is a possible line of Paschen series.

For n=6, the wavelength is 1093 nm, which falls in the infrared region and is a possible line of Paschen series.

For n=7, the wavelength is 1005 nm, which falls in the infrared region and is a possible line of Paschen series.

Therefore, there are 4 possible lines of Paschen series when the electron jumps from the 7th excited state to the ground state.

Answer

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