Part A Calulate the wavelengths (in nm) of the visible lines in the line spectru

Question

Part A Calulate the wavelengths (in nm) of the visible lines in the line spectrum of hydrogen using the Rydberg equation (nf = 2; ni = 3, 4, 5, and 6). Use three significant figures and order from shortest to longest wavelength. Part B Using Rydberg Part A Calulate the wavelengths (in nm) of the visible lines in the line spectrum of hydrogen using the Rydberg equation (nf = 2; ni = 3, 4, 5, and 6). Use three significant figures and order from shortest to longest wavelength. Part B Using Rydberg Part B Using Rydberg

Explanation / Answer

(A) The answer is: 410 nm, 434 nm, 486 nm, 656 nm

Rydberg equation: 1/wavelength = R(1/nf^2 - 1/ni^2)

where R is Rydberg constant, nf and ni are quantum numbers


When ni = 3

1/wavelength = 1.097 x 10^7 x (1/2^2 - 1/3^2) = 1523611 m-1

Wavelength = 1/1523611 = 6.56 x 10^(-7) m = 656 nm


When ni = 4

1/wavelength = 1.097 x 10^7 x (1/2^2 - 1/4^2) = 2056875 m-1

Wavelength = 1/2056875 = 4.86 x 10^(-7) m = 486 nm


When ni = 5

1/wavelength = 1.097 x 10^7 x (1/2^2 - 1/5^2) = 2303700 m-1

Wavelength = 1/2303700 = 4.34 x 10^(-7) m = 434 nm


When ni = 6

1/wavelength = 1.097 x 10^7 x (1/2^2 - 1/6^2) = 2437778 m-1

Wavelength = 1/2437778 = 4.10 x 10^(-7) m = 410 nm


(B) When ni = 3 and nf = 2

1/wavelength = 1.097 x 10^7 x (1/2^2 - 1/3^2) = 1523611 m-1

Wavelength = 1/1523611 = 6.56 x 10^(-7) m = 656 nm

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