What is the binding energy in eV of electrons in magnesium, if the longest-wavelength photon that can eject electrons is 337 nm?
frequency = velocity of light c / wavelength in meters
c = about 3 * 10^8 m/s
energy = Planck's constant * frequency
Plank's constant is 6.626 * 10^-24 Joule seconds
typo
6.626 * 10^-34 Joule seccondss
To determine the binding energy of electrons in magnesium, we can use the formula:
E = hc/λ - W
where E is the binding energy, h is the Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength of the photon, and W is the work function.
First, let's convert the wavelength from nanometers to meters:
337 nm = 337 x 10^-9 m
Now, let's calculate the binding energy:
E = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (337 x 10^-9 m) - W
To find the work function (W) for magnesium, we need to know the threshold energy (E_thresh) or the cutoff frequency (f_cutoff) for ejecting electrons.
The cutoff frequency can be calculated using the equation:
f_cutoff = c / λ_cutoff
Let's calculate the cutoff frequency for the given photon wavelength:
f_cutoff = 3.00 x 10^8 m/s / (337 x 10^-9 m)
Now, we need to find the threshold energy using the equation:
E_thresh = h * f_cutoff
E_thresh = 6.626 x 10^-34 J·s * (3.00 x 10^8 m/s / (337 x 10^-9 m))
Finally, we can substitute the calculated values back into the binding energy equation to find the answer:
E = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (337 x 10^-9 m) - E_thresh
The result will give you the binding energy in joules (J). To convert it to electron volts (eV), you can divide the result by the elementary charge (e), which is approximately 1.602 x 10^-19 C.
E (in eV) = E (in J) / (1.602 x 10^-19 C)