the complex ion[Ti(H2O)6]^3+ has a maximum absorption wavelength of 512 nm. Calculate the energy change in joules per ion.
Energy=planck'sconstant*speedoflight/wavelength
To calculate the energy change in joules per ion, we need to use the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength in meters.
First, convert the wavelength from nm to m:
λ = 512 nm = 512 x 10^-9 m.
Now we can calculate the energy change per ion:
E = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / (512 x 10^-9 m)
E ≈ 3.898 x 10^-19 J
Therefore, the energy change per ion is approximately 3.898 x 10^-19 Joules.
To calculate the energy change in joules per ion, we need to use the relation between wavelength, frequency, and energy.
First, let's convert the wavelength from nanometers to meters:
λ = 512 nm = 512 × 10^(-9) m
The speed of light, c, is approximately 3 × 10^8 m/s.
Now we can determine the frequency of the light using the equation:
c = λν
Rearranging the equation to solve for frequency, ν:
ν = c / λ
Plugging in the values, we find:
ν = (3 × 10^8 m/s) / (512 × 10^(-9) m) = (3 × 10^8) / (5.12 × 10^(-7)) Hz
Next, we need to convert the frequency to energy using Planck's equation:
E = hν
Where h is Planck's constant, approximately 6.626 × 10^(-34) J·s.
Using the equation:
E = (6.626 × 10^(-34) J·s) × [(3 × 10^8 Hz) / (5.12 × 10^(-7)) Hz]
Simplifying, we find:
E ≈ 1.227 × 10^(-19) J
Hence, the energy change in joules per ion is approximately 1.227 × 10^(-19) J.