The figure below depicts the first four energy levels in a hydrogen atom. The th

Question

The figure below depicts the first four energy levels in a hydrogen atom. The three transitions shown as amows emit ultraviolet light and occur at wavelengths of 121.566 nm, 102.583 nm, and 97.524 mm, respectively. Planck's constant is 6.62607 x 10 Jsand the speed oflight is 2.99792 x 10 m/s. a Find the frequency of light that would be emitted in a transition from the state labeled as n 4 to the state labeled as n 3. Frequency b Find the wavelength of light that would be emitted when a hydrogen atom undergoes the transition from the state labeled as n 4 to the state labeled as n -2 Express your Wavelength

Explanation / Answer

n = 4 to 3

En = -13.6/n^2 in eV

En = enrgy in nth orbit

E4 - E3 = -13.6 [ 1/4^2 - 1/3^2] = 0.66 eV

1 eV = 1.602*10^-19 J

0.66 eV = 1.05732*10^-19 J

E = hv

v = frequency

1.05732*10^-19 = 6.625*10^-34 *v

v = 1.59*10^14 Hz

b]

n=4 to n=2

E = E4-E2 = -13.6 [ 1/16 - 1/4 ] = 2.55 eV

2.55 eV = 4.0851*10^-19 J

E = hc / lambda

lambda = 486 nm

Ti - 22 --> 1s2 2s2 2p6 3s2 3p6 4s2 3d2 --> Ar [4s2 3d2]

K - 19 - 1s2 2s2 2p6 3s2 3p6 4s1 ---> Ar [4s1]

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