Question

Calculate the wavelengths (in nm) of the first 5 transitions in the Balmer series using the Rydberg equation. Convert the wavelengths calculated into frequencies.

Answer 1

Balmer series --> n = 2 so

n3 --> 2

n4 --> 2

n5 --> 2

N6 --> 2

n7 --> 2

Apply Rydberg Formula

E = R*(1/nf^2 – 1/ni ^2)

R = -2.178*10^-18 J

Nf = final stage/level

Ni = initial stage/level

E = Energy per unit (i.e. J/photon)

For the wavelength:

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = wavelength in meters

simplified:

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/nf^2 – 1/ni ^2)) * 10^9

since nf = 2, then

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/2^2 – 1/ni ^2)) * 10^9

n = 3,4,5,6,7,

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/2^2 – 1/3^2)) * 10^9 = 657 nm

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/2^2 – 1/4^2)) * 10^9 = 487 nm

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/2^2 – 1/5^2)) * 10^9 = 434 nm

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/2^2 – 1/6^2)) * 10^9 = 410 nm

WL = (6.626*10^-34 )(3*10^8) / ((2.178*10^-18) * (1/2^2 – 1/7^2)) * 10^9 = 398 nm

change to frequency

v(3) = c/WL*10^9 = (3*10^8)*(10^9)/(657 )= 4.56*10^14 Hz

v(4) = c/WL*10^9 = (3*10^8)*(10^9)/(487 )= 6.16*10^14 Hz

v(5) = c/WL*10^9 = (3*10^8)*(10^9)/(434 )= 6.91*10^14 Hz

v(6) = c/WL*10^9 = (3*10^8)*(10^9)/(410 )= 7.32*10^14 Hz

v() = c/WL*10^9 = (3*10^8)*(10^9)/(398)= 7.54*10^14 Hz