The frequency in per second of the radiation corresponding to n=5 is 6.9 * 10^14 s-1. The wavelength in nanometers of the line in the Balmer series corresponding to n=7 is 396 nm. The value of n corresponding to the Balmer series line at 380 nm is 10.
a) From the Rydberg formula;
1/λ = 1.097 * 10^7 m-1 (1/nf^2 - 1/ni^2)
Since this is the Balmer series, nf =2
1/λ = 1.097 * 10^7 m-1 (1/2^2 - 1/5^2)
1/λ = 1.097 * 10^7 m-1 (0.25 - 0.04)
1/λ = 1.097 * 10^7 m-1 (0.21)
λ = 4.34 * 10^-7 m
But
c = λf
c = speed of light, 3 * 10^8 m/s
f = 3 * 10^8 m/s/ 4.34 * 10^-7
f = 6.9 * 10^14 s-1
b) Again;
1/λ = 1.097 * 10^7 m-1 (1/nf^2 - 1/ni^2)
Since this is the Balmer series, nf =2
1/λ = 1.097 * 10^7 m-1 (1/2^2 - 1/7^2)
1/λ = 1.097 * 10^7 m-1 (0.25 - 0.02)
1/λ = 1.097 * 10^7 m-1 (0.23)
λ = 3.96 * 10^-7 m or 396 nm.
c) Again;
1/λ = 1.097 * 10^7 m-1 (1/nf^2 - 1/ni^2)
Since this is the Balmer series, nf =2
1/380 * 10^-9 = 1.097 * 10^7 (1/2^2 - 1/ni^2)
2631578.947 = 1.097 * 10^7 (1/2^2 - 1/ni^2)
2631578.947 /1.097 * 10^7 = (1/2^2 - 1/ni^2)
0.2399 = 0.25 - 1/ni^2
1/ni^2 = 0.25 - 0.2399
1/ni^2 = 0.0101
ni^2 = 99.0099
ni = 10
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