The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula: E = -Ry/n2
In this equation Ry stands for the Rydberg energy, and n stands for the principal quantum number of the orbital that holds the electron. Calculate the wavelength of the line in the absorption line spectrum of hydrogen caused by the transition of the electron from an orbital with n = 2 to an orbital with n = 8.

3.89002 × 10 ⁻⁷m = 389.002nm.

Explanation:

Without mincing words let's dive straight into the solution to the problem above. To calculate the wavelength of the line in the absorption line spectrum of hydrogen caused by the transition of the electron from an orbital with n = 2 to an orbital with n = 8, there is the need to make use of the change in energy equation.

The change in energy = 2.18 × 10⁻¹⁸ [ 1/2² - 1/8²] =  2.18 × 10⁻¹⁸ × [0.25 - 0.015625] =  2.18 × 10⁻¹⁸ × 0.234375 = 5.11 × 10⁻¹⁹.  

Therefore, the wavelength = plank's constant × speed of light/ change in energy = 6.626× 10⁻³⁴ × 3 × 10⁸/ 5.11 × 10⁻¹⁹ = 1.9878 × 10⁻²⁵/  5.11 × 10⁻¹⁹ = 0.389002 × 10⁻⁶ = 3.89002 × 10 ⁻⁷m = 389.002nm.

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