Calculating 5 Longest Lyman Series Wavelengths

[Tony11235]

How am supposed to calculate the five longest wavelengths of the Lyman series? What values of n are used? I see how you arrive at a definite limit as n goes to infinity, but the five longest? Sort of a dumb question.

 

[phucnv87]

Remember that

$$\Delta E=\frac{hc}{\lambda}$$

$$\Longrightarrow \lambda=\frac{hc}{\Delta E}$$

$$\Delta E=E_{initial}-E_{final}$$

To get the longest wavelength, $$\Delta E$$ must be at minimum value

 

[kyle8921]

Calculating the five longest wavelengths of the Lyman series involves using the Rydberg formula, which is given by 1/λ = R (1/n1^2 - 1/n2^2), where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

To calculate the five longest wavelengths, we must first determine the values of n that are used. The Lyman series involves transitions from higher energy levels to the ground state, so the values of n used will be n1 = 2, n2 = 1.

Using this information, we can plug in different values of n1 (starting with the highest value) into the Rydberg formula and solve for λ. The five longest wavelengths will be the results of these calculations.

It may seem like a "dumb" question, but it's always important to clarify any doubts or confusion in scientific calculations. I hope this explanation helps.