A potassium metal has a work function F = 4.41 x 10-19 J. Calculate the velocity of electrons emitted by exposing the metal to radiation of wavelength 300 nm.
calculate the incoming radiation energy=Planck'sConstant*speelight/wavelength
then subtract the work function.
Then convert the remaining energy to 1/2 m v^2, and find v.
To calculate the velocity of electrons emitted by exposing the potassium metal to radiation of a particular wavelength, we need to use the equation for the kinetic energy of emitted electrons.
The equation for the kinetic energy of emitted electrons is given by:
KE = hf - F
Where:
KE = Kinetic Energy of the emitted electron
h = Planck's constant (6.626 x 10^-34 J·s)
f = frequency of the radiation (speed of light / wavelength)
F = work function of the metal
First, let's calculate the frequency of the radiation using the speed of light and the given wavelength:
c = λv
Where:
c = speed of light (3 x 10^8 m/s)
λ = wavelength (in meters)
v = frequency
To convert the wavelength from nanometers to meters, we divide by 10^9:
λ = 300 nm / (10^9 m/nm) = 3 x 10^-7 m
Now, we can calculate the frequency:
v = c / λ = 3 x 10^8 m/s / 3 x 10^-7 m = 10^15 Hz
Next, we use the calculated frequency in the equation for the kinetic energy to find the velocity of the emitted electrons:
KE = hf - F
Since we are looking for the velocity (v), we can rearrange the equation to:
v = sqrt(2KE / m)
Where:
v = velocity of the emitted electron
KE = kinetic energy of the emitted electron
m = mass of the electron (9.11 x 10^-31 kg)
We can calculate the kinetic energy using the equation KE = hf - E = (6.626 x 10^-34 J·s)(10^15 Hz) - (4.41 x 10^-19 J) = 6.626 x 10^-19 J - 4.41 x 10^-19 J = 2.216 x 10^-19 J
Now, we can plug the kinetic energy and the mass of the electron into the equation to calculate the velocity:
v = sqrt(2KE / m) = sqrt(2(2.216 x 10^-19 J) / 9.11 x 10^-31 kg)
By evaluating this equation, we find that the velocity of the emitted electrons is approximately 2.488 x 10^6 m/s.