Calculate the energy (in eV) of the three lowest energy transitions in the Lyman series (the series that ends on n=1) of hydrogen. The wavelengths of these transitions are 121.6 nm, 102.6nm, and 97.3 nm. Draw an energy level diagram of these transitions
1/wavelength = R(1/n^2final - 1/n^2initial)
nfinal = lower level which is 1 in this case.
ninitial = upper level
We can't draw diagrams on the board but your should look something like this.
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To calculate the energy of the three lowest energy transitions in the Lyman series of hydrogen, you can use the formula:
E = (hc) / λ
Where:
E is the energy in eV
h is the Planck's constant (6.62607015 × 10^-34 J·s)
c is the speed of light (299,792,458 m/s)
λ is the wavelength of the transition in meters
First, we need to convert the wavelengths given in nanometers (nm) to meters (m):
Wavelength (in meters) = Wavelength (in nanometers) / 10^9
For the three transitions:
λ1 = 121.6 nm / 10^9 = 1.216 × 10^-7 m
λ2 = 102.6 nm / 10^9 = 1.026 × 10^-7 m
λ3 = 97.3 nm / 10^9 = 9.73 × 10^-8 m
Now, we can substitute these values into the formula to calculate the corresponding energies:
E1 = (hc) / λ1
E2 = (hc) / λ2
E3 = (hc) / λ3
Using the given values for h and c, we can solve for E1, E2, and E3:
E1 = (6.62607015 × 10^-34 J·s × 299,792,458 m/s) / (1.216 × 10^-7 m)
E2 = (6.62607015 × 10^-34 J·s × 299,792,458 m/s) / (1.026 × 10^-7 m)
E3 = (6.62607015 × 10^-34 J·s × 299,792,458 m/s) / (9.73 × 10^-8 m)
Calculating these values will give you the energies of the three transitions in Joules (J). To convert them to electron volts (eV), you can use the conversion factor 1 eV = 1.602176634 × 10^-19 J.
Finally, to draw an energy-level diagram of these transitions, you can represent the energy levels as horizontal lines, with the lowest level (n=1) at the bottom. Label the energy of each level according to the calculated values, starting from the ground state energy (n=1) and going upwards for higher energy levels. Draw arrows connecting the energy levels representing the transitions, with the wavelengths written next to the respective arrows.