If, in 1/lambda = R_y (1/n_1^2 - 1/n_2^2), you set n_1 = 1 and take n_2 greater

Question

If, in 1/lambda = R_y (1/n_1^2 - 1/n_2^2), you set n_1 = 1 and take n_2 greater than 1, you generate what is known as the Lyman series. Find the wavelength of the first member of this series. The value of h is 1.05457 times 10^-34 J middot s; the Rydberg constant for hydrogen is 1.09735 times 10^7 m^-1; the Bohr radius is 5.29177 times 10^-11 m; and the ground state energy for hydrogen is 13.6057 eV. Answer in units of nm. Consider the next three members of this series. The wavelengths of successive members of the Lyman series approach a common limit as n_2 rightarrow infinity. What is this limit? Answer in units of nm.

Explanation / Answer

005) for first member

n1 = 1, n2 = 2

1/lamda = R*(1/n1^2 - 1/n2^2)

1/lamda = 1.09735*10^7*(1/1^2 - 1/2^2)

lamda = 121.5 nm <<<------------Answer

006)

n1 = 1, n2 = infinite

1/lamda = R*(1/n1^2 - 1/n2^2)

1/lamda = 1.09735*10^7*(1/1^2) - 1/infinite^2)

lamda = 91.1 nm <<<------------Answer

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