Question

Calculate the wavelength of the line in the emission line spectrum of hydrogen caused by the transition of the electron from an orbital with =n8 to an orbital with =n1. Round your answer to 3 significant digits. in nm

Answer 1

The wavelength of the emission line caused by the electron transition from n=8 to n=1 in hydrogen is 1320 nm, rounded to 3 significant figures.

Step-by-step explanation:

Here are the steps to solve this problem:

1) We are given that the electron is transitioning from an orbital n=8 to n=1 in the emission spectrum of hydrogen.

2) According to the Rydberg formula for hydrogen, the wavelength of an emission line is given by:

λ = 1240/ (1/n^2_f - 1/n^2_i) nm

Where:

n_f is the final orbital (1 in this case)

n_i is the initial orbital (8 in this case)

3) Plugging in the values n_f = 1 and n_i = 8 into the Rydberg formula, we get:

λ = 1240/ (1/1^2 - 1/8^2)

= 1240/(1 - 0.0625)

= 1240/0.9375

= 1324 nm

4) Rounding this to 3 significant figures gives:

1320 nm

So the final answer is:

1320 nm