Question

Please show the work to the following:

1a) A hydrogen electron transitions from ni= 4 to nf= 9. What is the change in energy associated with this transition? Is the energy released or absorbed?

1b) A hydrogen electron transitions from ni= 4 to nf=9. What is the wavelength associated with this transition? remember 63 had you calculate the frequency!)

1c) A hydrogen electron transitions from ni= 2 to nf= 1. What is the wavelength associated with this transition?

1d) A hydrogen electron transitions from ni= 3 to nf= 1. What is the wavelength associated with this transition?

1e) A hydrogen electron transitions from ni= 4 to nf= 1. What is the wavelength associated with this transition?

Answer 1

1) a ni = 4 and nf = 9

1/ = -R (1/nf² - 1/ni²)    R = Rydberg constant = 1.0974 x 10⁷ /m

1/ = -1.0974 x 10⁷ (1/9² - 1/4²)

1/ = -1.0974 x 10⁷ ( -65 /1296)

1/ = -71.331 x 10⁷/1296 = 0.0550 x 10⁷ /m

= 18.2 x 10^-7 m

Frequency, f = C/ = 3 x 10⁸ m/s / 18.2 x 10^-7 m = 0.165 X 10¹⁵ /s = 165 x 10¹³ /s

deltaE = hc/

deltaE = 6.625 x 10^-34 J x 3 x 10⁸ m/s / 18.2 x 10^-7 m

Change in energy, E = 1.092 x 10^-19 J

Energy will be absorbed as there is transition from lower energy state to higher energy state and energy difference is positive

2) nf = 1 and ni = 2

1/ = -R (1/nf² - 1/ni²)    R = Rydberg constant = 1.0974 x 10⁷ /m

1/ = - 1.0974 x 10⁷ /m (1/1² - 1/2²)

1/ = -1.0974 x 10⁷ /m (3/4)

1/ = 0.82305 x 10⁷ /m

= 1/0.82305 x 10⁷ /m = 1.215 x 10^-7 m

3) nf = 1 and ni = 3

1/ = -R (1/nf² - 1/ni²)    R = Rydberg constant = 1.0974 x 10⁷ /m

1/ = - 1.0974 x 10⁷ /m (1/1² - 1/3²)

1/ = -1.0974 x 10⁷ /m (8/9)

1/ = 0.9755 x 10⁷ /m

= 1/0.9755 x 10⁷ /m = 1.025 x 10^-7 m

4) nf = 1 and ni = 4

1/ = -R (1/nf² - 1/ni²)    R = Rydberg constant = 1.0974 x 10⁷ /m

1/ = - 1.0974 x 10⁷ /m (1/1² - 1/4²)

1/ = -1.0974 x 10⁷ /m (15/16)

1/ = 1.029 x 10⁷ /m

= 1/1.029 x 10⁷ /m = 0.972 x 10^-7 m